LMFDB - Embedded newform 158.2.e.a.67.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [158,2,Mod(21,158)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("158.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(158, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 158 = 2 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	158.e (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.26163635194$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			67.4
Character	$\chi$	$=$	158.67
Dual form			158.2.e.a.125.4

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.120537 + 0.992709i) q^{2} +(0.592124 - 1.56130i) q^{3} +(-0.970942 + 0.239316i) q^{4} +(1.43820 + 0.754826i) q^{5} +(1.62129 + 0.399613i) q^{6} +(1.16412 - 3.06952i) q^{7} +(-0.354605 - 0.935016i) q^{8} +(0.158475 + 0.140397i) q^{9} +(-0.575967 + 1.51870i) q^{10} +(-4.50880 + 2.36640i) q^{11} +(-0.201274 + 1.65764i) q^{12} +(5.00360 - 1.23328i) q^{13} +(3.18746 + 0.785638i) q^{14} +(2.03011 - 1.79852i) q^{15} +(0.885456 - 0.464723i) q^{16} +(2.77682 - 0.684425i) q^{17} +(-0.120271 + 0.174243i) q^{18} +(-4.40467 + 6.38127i) q^{19} +(-1.57705 - 0.388708i) q^{20} +(-4.10315 - 3.63507i) q^{21} +(-2.89262 - 4.19068i) q^{22} -7.48530 q^{23} -1.66981 q^{24} +(-1.34166 - 1.94374i) q^{25} +(1.82740 + 4.81846i) q^{26} +(4.74868 - 2.49230i) q^{27} +(-0.395704 + 3.25892i) q^{28} +(-4.74512 + 4.20381i) q^{29} +(2.03011 + 1.79852i) q^{30} +(-0.247468 - 2.03808i) q^{31} +(0.568065 + 0.822984i) q^{32} +(1.02490 + 8.44080i) q^{33} +(1.01414 + 2.67408i) q^{34} +(3.99118 - 3.53588i) q^{35} +(-0.187469 - 0.0983915i) q^{36} +(-1.64687 + 2.38591i) q^{37} +(-6.86567 - 3.60338i) q^{38} +(1.03723 - 8.54238i) q^{39} +(0.195782 - 1.61241i) q^{40} +(-5.04424 - 2.64742i) q^{41} +(3.11399 - 4.51139i) q^{42} +(-4.03792 - 2.11926i) q^{43} +(3.81146 - 3.37666i) q^{44} +(0.121944 + 0.321540i) q^{45} +(-0.902254 - 7.43073i) q^{46} +(2.26736 + 3.28484i) q^{47} +(-0.201274 - 1.65764i) q^{48} +(-2.82721 - 2.50469i) q^{49} +(1.76784 - 1.56617i) q^{50} +(0.575629 - 4.74073i) q^{51} +(-4.56306 + 2.39488i) q^{52} +(1.47620 + 3.89243i) q^{53} +(3.04652 + 4.41364i) q^{54} -8.27077 q^{55} -3.28285 q^{56} +(7.35498 + 10.6555i) q^{57} +(-4.74512 - 4.20381i) q^{58} +(7.26346 + 1.79028i) q^{59} +(-1.54070 + 2.23209i) q^{60} +(5.10493 - 7.39577i) q^{61} +(1.99339 - 0.491326i) q^{62} +(0.615434 - 0.323005i) q^{63} +(-0.748511 + 0.663123i) q^{64} +(8.12709 + 2.00315i) q^{65} +(-8.25572 + 2.03485i) q^{66} +(0.628249 - 5.17410i) q^{67} +(-2.53234 + 1.32907i) q^{68} +(-4.43223 + 11.6868i) q^{69} +(3.99118 + 3.53588i) q^{70} +(3.80227 + 10.0257i) q^{71} +(0.0750772 - 0.197962i) q^{72} +(-6.89047 - 1.69835i) q^{73} +(-2.56702 - 1.34728i) q^{74} +(-3.82919 + 0.943811i) q^{75} +(2.74954 - 7.24995i) q^{76} +(2.01495 + 16.5946i) q^{77} +8.60512 q^{78} +(6.89199 + 5.61252i) q^{79} +1.62425 q^{80} +(-1.00287 - 8.25935i) q^{81} +(2.02010 - 5.32658i) q^{82} +(13.2315 - 3.26128i) q^{83} +(4.85385 + 2.54750i) q^{84} +(4.51025 + 1.11168i) q^{85} +(1.61709 - 4.26392i) q^{86} +(3.75372 + 9.89775i) q^{87} +(3.81146 + 3.37666i) q^{88} +(-0.560917 + 1.47902i) q^{89} +(-0.304497 + 0.159812i) q^{90} +(2.03920 - 16.7943i) q^{91} +(7.26779 - 1.79135i) q^{92} +(-3.32859 - 0.820424i) q^{93} +(-2.98759 + 2.64677i) q^{94} +(-11.1516 + 5.85279i) q^{95} +(1.62129 - 0.399613i) q^{96} +(-1.77080 + 2.56545i) q^{97} +(2.14564 - 3.10850i) q^{98} +(-1.04677 - 0.258005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 8 q^{7} - 4 q^{8} - 18 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{12} + 16 q^{13} + 5 q^{14} - 2 q^{15} - 4 q^{16} + 6 q^{17} - 18 q^{18} + 6 q^{19} - 2 q^{20}+ \cdots - 58 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 8 * q^7 - 4 * q^8 - 18 * q^9 - 2 * q^10 - 8 * q^11 - 2 * q^12 + 16 * q^13 + 5 * q^14 - 2 * q^15 - 4 * q^16 + 6 * q^17 - 18 * q^18 + 6 * q^19 - 2 * q^20 - 12 * q^21 + 5 * q^22 - 16 * q^23 + 24 * q^24 - 17 * q^25 + 3 * q^26 + 7 * q^27 - 8 * q^28 - 34 * q^29 - 2 * q^30 - 19 * q^31 - 4 * q^32 + 8 * q^33 - 20 * q^34 + 122 * q^35 - 18 * q^36 - 4 * q^37 - 20 * q^38 - 50 * q^39 - 2 * q^40 - 36 * q^41 + 14 * q^42 - 24 * q^43 + 18 * q^44 - 4 * q^45 + 10 * q^46 - 22 * q^47 - 2 * q^48 - 28 * q^49 - 4 * q^50 + 78 * q^51 - 10 * q^52 - 12 * q^53 + 7 * q^54 - 88 * q^55 + 18 * q^56 - 28 * q^57 - 34 * q^58 - 52 * q^59 + 11 * q^60 - 47 * q^61 + 20 * q^62 + 11 * q^63 - 4 * q^64 - 16 * q^65 + 8 * q^66 + 67 * q^67 - 7 * q^68 - 4 * q^69 + 122 * q^70 - 12 * q^71 - 18 * q^72 + 101 * q^73 - 4 * q^74 - 62 * q^75 + 32 * q^76 + 113 * q^77 - 50 * q^78 - 2 * q^80 + 36 * q^81 + 29 * q^82 + 91 * q^83 + 53 * q^84 - q^85 - 24 * q^86 + 210 * q^87 + 18 * q^88 + 4 * q^89 + 126 * q^90 - 33 * q^91 - 3 * q^92 - 3 * q^93 + 17 * q^94 - 42 * q^95 - 2 * q^96 - 32 * q^97 + 24 * q^98 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/158\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{13}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.120537	+	0.992709i	0.0852323	+	0.701951i
$2$	0.120537	+	0.992709i	0.0852323	+	0.701951i
$3$	0.592124	−	1.56130i	0.341863	−	0.901419i	−0.648285	−	0.761397i	$-0.724514\pi$
$3$	0.592124	−	1.56130i	0.341863	−	0.901419i	0.990148	−	0.140021i	$-0.0447172\pi$
$4$	−0.970942	+	0.239316i	−0.485471	+	0.119658i
$5$	1.43820	+	0.754826i	0.643183	+	0.337569i	0.754581	−	0.656207i	$-0.227840\pi$
$5$	1.43820	+	0.754826i	0.643183	+	0.337569i	−0.111398	+	0.993776i	$0.535533\pi$
$6$	1.62129	+	0.399613i	0.661890	+	0.163141i
$7$	1.16412	−	3.06952i	0.439994	−	1.16017i	−0.513322	−	0.858196i	$-0.671585\pi$
$7$	1.16412	−	3.06952i	0.439994	−	1.16017i	0.953316	−	0.301973i	$-0.0976453\pi$
$8$	−0.354605	−	0.935016i	−0.125372	−	0.330578i
$9$	0.158475	+	0.140397i	0.0528251	+	0.0467989i
$10$	−0.575967	+	1.51870i	−0.182137	+	0.480255i
$11$	−4.50880	+	2.36640i	−1.35945	+	0.713496i	−0.977549	−	0.210706i	$-0.932424\pi$
$11$	−4.50880	+	2.36640i	−1.35945	+	0.713496i	−0.381904	+	0.924202i	$0.624731\pi$
$12$	−0.201274	+	1.65764i	−0.0581028	+	0.478519i
$13$	5.00360	−	1.23328i	1.38775	−	0.342049i	0.526474	−	0.850191i	$-0.323514\pi$
$13$	5.00360	−	1.23328i	1.38775	−	0.342049i	0.861273	+	0.508142i	$0.169667\pi$
$14$	3.18746	+	0.785638i	0.851884	+	0.209970i
$15$	2.03011	−	1.79852i	0.524171	−	0.464375i
$16$	0.885456	−	0.464723i	0.221364	−	0.116181i
$17$	2.77682	−	0.684425i	0.673478	−	0.165998i	0.112277	−	0.993677i	$-0.464186\pi$
$17$	2.77682	−	0.684425i	0.673478	−	0.165998i	0.561201	+	0.827679i	$0.310339\pi$
$18$	−0.120271	+	0.174243i	−0.0283482	+	0.0410694i
$19$	−4.40467	+	6.38127i	−1.01050	+	1.46396i	−0.129079	+	0.991634i	$0.541202\pi$
$19$	−4.40467	+	6.38127i	−1.01050	+	1.46396i	−0.881422	+	0.472329i	$0.843413\pi$
$20$	−1.57705	−	0.388708i	−0.352639	−	0.0869178i
$21$	−4.10315	−	3.63507i	−0.895381	−	0.793238i
$22$	−2.89262	−	4.19068i	−0.616709	−	0.893457i
$23$	−7.48530			−1.56079			−0.780397	−	0.625285i	$-0.784983\pi$
$23$	−7.48530			−1.56079			−0.780397	+	0.625285i	$0.784983\pi$
$24$	−1.66981			−0.340849
$25$	−1.34166	−	1.94374i	−0.268333	−	0.388747i
$26$	1.82740	+	4.81846i	0.358383	+	0.944978i
$27$	4.74868	−	2.49230i	0.913884	−	0.479643i
$28$	−0.395704	+	3.25892i	−0.0747810	+	0.615877i
$29$	−4.74512	+	4.20381i	−0.881147	+	0.780628i	−0.976658	−	0.214800i	$-0.931090\pi$
$29$	−4.74512	+	4.20381i	−0.881147	+	0.780628i	0.0955109	+	0.995428i	$0.469552\pi$
$30$	2.03011	+	1.79852i	0.370645	+	0.328363i
$31$	−0.247468	−	2.03808i	−0.0444465	−	0.366050i	−0.997914	−	0.0645545i	$-0.979437\pi$
$31$	−0.247468	−	2.03808i	−0.0444465	−	0.366050i	0.953468	−	0.301495i	$-0.0974857\pi$
$32$	0.568065	+	0.822984i	0.100421	+	0.145484i
$33$	1.02490	+	8.44080i	0.178412	+	1.46935i
$34$	1.01414	+	2.67408i	0.173924	+	0.458601i
$35$	3.99118	−	3.53588i	0.674633	−	0.597673i
$36$	−0.187469	−	0.0983915i	−0.0312449	−	0.0163986i
$37$	−1.64687	+	2.38591i	−0.270745	+	0.392241i	−0.934646	−	0.355579i	$-0.884284\pi$
$37$	−1.64687	+	2.38591i	−0.270745	+	0.392241i	0.663902	+	0.747820i	$0.268899\pi$
$38$	−6.86567	−	3.60338i	−1.11376	−	0.584545i
$39$	1.03723	−	8.54238i	0.166090	−	1.36788i
$40$	0.195782	−	1.61241i	0.0309558	−	0.254944i
$41$	−5.04424	−	2.64742i	−0.787779	−	0.413458i	0.0223207	−	0.999751i	$-0.492895\pi$
$41$	−5.04424	−	2.64742i	−0.787779	−	0.413458i	−0.810099	+	0.586293i	$0.800587\pi$
$42$	3.11399	−	4.51139i	0.480499	−	0.696123i
$43$	−4.03792	−	2.11926i	−0.615776	−	0.323184i	0.127836	−	0.991795i	$-0.459197\pi$
$43$	−4.03792	−	2.11926i	−0.615776	−	0.323184i	−0.743612	+	0.668611i	$0.766889\pi$
$44$	3.81146	−	3.37666i	0.574600	−	0.509051i
$45$	0.121944	+	0.321540i	0.0181784	+	0.0479324i
$46$	−0.902254	−	7.43073i	−0.133030	−	1.09560i
$47$	2.26736	+	3.28484i	0.330728	+	0.479143i	0.952707	−	0.303892i	$-0.0982861\pi$
$47$	2.26736	+	3.28484i	0.330728	+	0.479143i	−0.621978	+	0.783035i	$0.713671\pi$
$48$	−0.201274	−	1.65764i	−0.0290514	−	0.239260i
$49$	−2.82721	−	2.50469i	−0.403887	−	0.357813i
$50$	1.76784	−	1.56617i	0.250011	−	0.221490i
$51$	0.575629	−	4.74073i	0.0806041	−	0.663835i
$52$	−4.56306	+	2.39488i	−0.632782	+	0.332110i
$53$	1.47620	+	3.89243i	0.202772	+	0.534667i	0.997371	−	0.0724689i	$-0.0230878\pi$
$53$	1.47620	+	3.89243i	0.202772	+	0.534667i	−0.794598	+	0.607135i	$0.792319\pi$
$54$	3.04652	+	4.41364i	0.414579	+	0.600621i
$55$	−8.27077			−1.11523
$56$	−3.28285			−0.438689
$57$	7.35498	+	10.6555i	0.974191	+	1.41136i
$58$	−4.74512	−	4.20381i	−0.623065	−	0.551988i
$59$	7.26346	+	1.79028i	0.945622	+	0.233075i	0.681835	−	0.731506i	$-0.261182\pi$
$59$	7.26346	+	1.79028i	0.945622	+	0.233075i	0.263787	+	0.964581i	$0.415028\pi$
$60$	−1.54070	+	2.23209i	−0.198904	+	0.288162i
$61$	5.10493	−	7.39577i	0.653620	−	0.946932i	−0.346341	−	0.938109i	$-0.612576\pi$
$61$	5.10493	−	7.39577i	0.653620	−	0.946932i	0.999961	−	0.00882332i	$-0.00280859\pi$
$62$	1.99339	−	0.491326i	0.253161	−	0.0623985i
$63$	0.615434	−	0.323005i	0.0775374	−	0.0406948i
$64$	−0.748511	+	0.663123i	−0.0935638	+	0.0828903i
$65$	8.12709	+	2.00315i	1.00804	+	0.248460i
$66$	−8.25572	+	2.03485i	−1.01621	+	0.250473i
$67$	0.628249	−	5.17410i	0.0767529	−	0.632117i	−0.902675	−	0.430323i	$-0.858400\pi$
$67$	0.628249	−	5.17410i	0.0767529	−	0.632117i	0.979428	−	0.201794i	$-0.0646771\pi$
$68$	−2.53234	+	1.32907i	−0.307091	+	0.161174i
$69$	−4.43223	+	11.6868i	−0.533578	+	1.40693i
$70$	3.99118	+	3.53588i	0.477038	+	0.422619i
$71$	3.80227	+	10.0257i	0.451246	+	1.18984i	0.946960	+	0.321352i	$0.104137\pi$
$71$	3.80227	+	10.0257i	0.451246	+	1.18984i	−0.495714	+	0.868486i	$0.665094\pi$
$72$	0.0750772	−	0.197962i	0.00884793	−	0.0233301i
$73$	−6.89047	−	1.69835i	−0.806469	−	0.198777i	−0.185533	−	0.982638i	$-0.559401\pi$
$73$	−6.89047	−	1.69835i	−0.806469	−	0.198777i	−0.620936	+	0.783861i	$0.713247\pi$
$74$	−2.56702	−	1.34728i	−0.298410	−	0.156618i
$75$	−3.82919	+	0.943811i	−0.442157	+	0.108982i
$76$	2.74954	−	7.24995i	0.315394	−	0.831626i
$77$	2.01495	+	16.5946i	0.229625	+	1.89113i
$78$	8.60512			0.974339
$79$	6.89199	+	5.61252i	0.775410	+	0.631458i
$79$	6.89199	+	5.61252i	0.775410	+	0.631458i
$80$	1.62425			0.181597
$81$	−1.00287	−	8.25935i	−0.111430	−	0.917706i
$82$	2.02010	−	5.32658i	0.223083	−	0.588222i
$83$	13.2315	−	3.26128i	1.45235	−	0.357972i	0.567317	−	0.823500i	$-0.307982\pi$
$83$	13.2315	−	3.26128i	1.45235	−	0.357972i	0.885033	+	0.465528i	$0.154135\pi$
$84$	4.85385	+	2.54750i	0.529598	+	0.277955i
$85$	4.51025	+	1.11168i	0.489205	+	0.120578i
$86$	1.61709	−	4.26392i	0.174376	−	0.459791i
$87$	3.75372	+	9.89775i	0.402441	+	1.06115i
$88$	3.81146	+	3.37666i	0.406303	+	0.359953i
$89$	−0.560917	+	1.47902i	−0.0594571	+	0.156776i	−0.961453	−	0.274969i	$-0.911332\pi$
$89$	−0.560917	+	1.47902i	−0.0594571	+	0.156776i	0.901996	+	0.431744i	$0.142102\pi$
$90$	−0.304497	+	0.159812i	−0.0320968	+	0.0168457i
$91$	2.03920	−	16.7943i	0.213766	−	1.76052i
$92$	7.26779	−	1.79135i	0.757720	−	0.186761i
$93$	−3.32859	−	0.820424i	−0.345159	−	0.0850740i
$94$	−2.98759	+	2.64677i	−0.308146	+	0.272994i
$95$	−11.1516	+	5.85279i	−1.14413	+	0.600483i
$96$	1.62129	−	0.399613i	0.165472	−	0.0407853i
$97$	−1.77080	+	2.56545i	−0.179798	+	0.260482i	−0.902512	−	0.430665i	$-0.858279\pi$
$97$	−1.77080	+	2.56545i	−0.179798	+	0.260482i	0.722714	+	0.691147i	$0.242894\pi$
$98$	2.14564	−	3.10850i	0.216743	−	0.314006i
$99$	−1.04677	−	0.258005i	−0.105204	−	0.0259305i
$100$	1.76784	+	1.56617i	0.176784	+	0.156617i
$101$	4.52026	+	6.54873i	0.449783	+	0.651623i	0.980636	−	0.195841i	$-0.0627436\pi$
$101$	4.52026	+	6.54873i	0.449783	+	0.651623i	−0.530853	+	0.847464i	$0.678128\pi$
$102$	4.77555			0.472850
$103$	−8.76461			−0.863603			−0.431801	−	0.901969i	$-0.642122\pi$
$103$	−8.76461			−0.863603			−0.431801	+	0.901969i	$0.642122\pi$
$104$	−2.92743	−	4.24112i	−0.287058	−	0.415876i
$105$	−3.15731	−	8.32513i	−0.308121	−	0.812450i
$106$	−3.68611	+	1.93462i	−0.358027	+	0.187907i
$107$	0.863449	−	7.11114i	0.0834728	−	0.687460i	−0.889564	−	0.456810i	$-0.848992\pi$
$107$	0.863449	−	7.11114i	0.0834728	−	0.687460i	0.973037	−	0.230650i	$-0.0740851\pi$
$108$	−4.01425	+	3.55631i	−0.386271	+	0.342206i
$109$	1.48818	+	1.31841i	0.142542	+	0.126281i	0.731381	−	0.681970i	$-0.238876\pi$
$109$	1.48818	+	1.31841i	0.142542	+	0.126281i	−0.588839	+	0.808250i	$0.700415\pi$
$110$	−0.996932	−	8.21047i	−0.0950537	−	0.782838i
$111$	2.74997	+	3.98403i	0.261016	+	0.378147i
$112$	−0.395704	−	3.25892i	−0.0373905	−	0.307939i
$113$	−4.05040	−	10.6800i	−0.381029	−	1.00469i	−0.979124	−	0.203266i	$-0.934844\pi$
$113$	−4.05040	−	10.6800i	−0.381029	−	1.00469i	0.598094	−	0.801426i	$-0.295925\pi$
$114$	−9.69130	+	8.58574i	−0.907673	+	0.804128i
$115$	−10.7654	−	5.65010i	−1.00388	−	0.526875i
$116$	3.60120	−	5.21724i	0.334363	−	0.484408i
$117$	0.966094	+	0.507045i	0.0893154	+	0.0468764i
$118$	−0.901715	+	7.42630i	−0.0830096	+	0.683646i
$119$	1.13168	−	9.32026i	0.103741	−	0.854387i
$120$	−2.40153	−	1.26042i	−0.219229	−	0.115060i
$121$	8.48068	−	12.2864i	0.770971	−	1.11694i
$122$	7.95718	+	4.17625i	0.720410	+	0.378100i
$123$	−7.12025	+	6.30799i	−0.642011	+	0.568772i
$124$	0.728021	+	1.91963i	0.0653782	+	0.172388i
$125$	−1.44131	−	11.8702i	−0.128914	−	1.06171i
$126$	0.394832	+	0.572013i	0.0351744	+	0.0509590i
$127$	−0.263324	−	2.16867i	−0.0233662	−	0.192438i	0.976352	−	0.216188i	$-0.0693625\pi$
$127$	−0.263324	−	2.16867i	−0.0233662	−	0.192438i	−0.999718	+	0.0237502i	$0.992439\pi$
$128$	−0.748511	−	0.663123i	−0.0661596	−	0.0586123i
$129$	−5.69976	+	5.04955i	−0.501836	+	0.444588i
$130$	−1.00893	+	8.30928i	−0.0884890	+	0.728772i
$131$	−0.805736	+	0.422883i	−0.0703975	+	0.0369475i	−0.499555	−	0.866282i	$-0.666503\pi$
$131$	−0.805736	+	0.422883i	−0.0703975	+	0.0369475i	0.429157	+	0.903230i	$0.358811\pi$
$132$	−3.01513	−	7.95025i	−0.262434	−	0.691981i
$133$	14.4599	+	20.9488i	1.25383	+	1.81649i
$134$	5.21210			0.450257
$135$	8.71081			0.749707
$136$	−1.62462	−	2.35367i	−0.139310	−	0.201826i
$137$	−13.5448	−	11.9996i	−1.15721	−	1.02520i	−0.999287	−	0.0377451i	$-0.987983\pi$
$137$	−13.5448	−	11.9996i	−1.15721	−	1.02520i	−0.157921	−	0.987452i	$-0.550479\pi$
$138$	−12.1359	−	2.99122i	−1.03307	−	0.254630i
$139$	9.29429	−	13.4651i	0.788331	−	1.14210i	−0.198461	−	0.980109i	$-0.563594\pi$
$139$	9.29429	−	13.4651i	0.788331	−	1.14210i	0.986793	−	0.161987i	$-0.0517902\pi$
$140$	−3.02902	+	4.38829i	−0.255999	+	0.370878i
$141$	6.47119	−	1.59500i	0.544972	−	0.134324i
$142$	−9.49434	+	4.98301i	−0.796747	+	0.418165i
$143$	−19.6418	+	17.4011i	−1.64253	+	1.45515i
$144$	0.205569	+	0.0506681i	0.0171307	+	0.00422234i
$145$	−9.99759	+	2.46418i	−0.830254	+	0.204639i
$146$	0.855412	−	7.04495i	0.0707944	−	0.583044i
$147$	−5.58464	+	2.93104i	−0.460613	+	0.241748i
$148$	1.02803	−	2.71070i	0.0845039	−	0.222818i
$149$	−1.82014	−	1.61250i	−0.149112	−	0.132101i	0.585269	−	0.810839i	$-0.300989\pi$
$149$	−1.82014	−	1.61250i	−0.149112	−	0.132101i	−0.734381	+	0.678738i	$0.762527\pi$
$150$	−1.39849	−	3.68751i	−0.114186	−	0.301084i
$151$	6.24814	−	16.4750i	0.508466	−	1.34071i	−0.397592	−	0.917562i	$-0.630154\pi$
$151$	6.24814	−	16.4750i	0.508466	−	1.34071i	0.906058	−	0.423153i	$-0.139077\pi$
$152$	7.52851	+	1.85561i	0.610643	+	0.150510i
$153$	0.536149	+	0.281393i	0.0433451	+	0.0227492i
$154$	−16.2307	+	4.00051i	−1.30791	+	0.322371i
$155$	1.18249	−	3.11796i	0.0949796	−	0.250441i
$156$	1.03723	+	8.54238i	0.0830451	+	0.683938i
$157$	−1.73610			−0.138556			−0.0692780	−	0.997597i	$-0.522070\pi$
$157$	−1.73610			−0.138556			−0.0692780	+	0.997597i	$0.522070\pi$
$158$	−4.74086	+	7.51826i	−0.377163	+	0.598121i
$159$	6.95136			0.551279
$160$	0.195782	+	1.61241i	0.0154779	+	0.127472i
$161$	−8.71375	+	22.9763i	−0.686740	+	1.81078i
$162$	8.07825	−	1.99111i	0.634687	−	0.156436i
$163$	13.1472	+	6.90017i	1.02977	+	0.540463i	0.892960	−	0.450135i	$-0.148624\pi$
$163$	13.1472	+	6.90017i	1.02977	+	0.540463i	0.136805	+	0.990598i	$0.456317\pi$
$164$	5.53124	+	1.36333i	0.431917	+	0.106458i
$165$	−4.89733	+	12.9132i	−0.381256	+	1.00529i
$166$	4.83239	+	12.7420i	0.375066	+	0.988968i
$167$	−4.78228	−	4.23673i	−0.370064	−	0.327848i	0.457510	−	0.889204i	$-0.348741\pi$
$167$	−4.78228	−	4.23673i	−0.370064	−	0.327848i	−0.827574	+	0.561356i	$0.810280\pi$
$168$	−1.94386	+	5.12553i	−0.149972	+	0.395443i
$169$	12.0041	−	6.30023i	0.923391	−	0.484633i
$170$	−0.559921	+	4.61136i	−0.0429440	+	0.353676i
$171$	−1.59394	+	0.392871i	−0.121892	+	0.0300436i
$172$	4.42775	+	1.09134i	0.337613	+	0.0832141i
$173$	8.55261	−	7.57695i	0.650243	−	0.576065i	−0.272180	−	0.962246i	$-0.587745\pi$
$173$	8.55261	−	7.57695i	0.650243	−	0.576065i	0.922423	+	0.386181i	$0.126206\pi$
$174$	−9.37313	+	4.91940i	−0.710575	+	0.372938i
$175$	−7.52819	+	1.85553i	−0.569077	+	0.140265i
$176$	−2.89262	+	4.19068i	−0.218039	+	0.315885i
$177$	7.09604	−	10.2804i	0.533371	−	0.772722i
$178$	−1.53585	−	0.378552i	−0.115116	−	0.0283737i
$179$	3.75914	+	3.33031i	0.280971	+	0.248919i	0.791824	−	0.610749i	$-0.209132\pi$
$179$	3.75914	+	3.33031i	0.280971	+	0.248919i	−0.510853	+	0.859668i	$0.670670\pi$
$180$	−0.195350	−	0.283014i	−0.0145605	−	0.0210946i
$181$	−24.8523			−1.84726			−0.923629	−	0.383287i	$-0.874792\pi$
$181$	−24.8523			−1.84726			−0.923629	+	0.383287i	$0.874792\pi$
$182$	16.9177			1.25402
$183$	−8.52429	−	12.3496i	−0.630134	−	0.912906i
$184$	2.65433	+	6.99888i	0.195679	+	0.515964i
$185$	−4.16948	+	2.18831i	−0.306547	+	0.160888i
$186$	0.413225	−	3.40321i	0.0302991	−	0.249536i
$187$	−10.9005	+	9.65700i	−0.797124	+	0.706190i
$188$	−2.98759	−	2.64677i	−0.217892	−	0.193036i
$189$	−2.12215	−	17.4775i	−0.154364	−	1.27130i
$190$	−7.15428	−	10.3648i	−0.519026	−	0.751939i
$191$	−2.31589	−	19.0731i	−0.167572	−	1.38008i	−0.797450	−	0.603385i	$-0.793818\pi$
$191$	−2.31589	−	19.0731i	−0.167572	−	1.38008i	0.629878	−	0.776694i	$-0.283105\pi$
$192$	0.592124	+	1.56130i	0.0427329	+	0.112677i
$193$	−1.95629	+	1.73312i	−0.140817	+	0.124753i	−0.730591	−	0.682815i	$-0.760755\pi$
$193$	−1.95629	+	1.73312i	−0.140817	+	0.124753i	0.589774	+	0.807568i	$0.299217\pi$
$194$	−2.76019	−	1.44866i	−0.198170	−	0.104008i
$195$	7.93976	−	11.5027i	0.568578	−	0.823728i
$196$	3.34447	+	1.75531i	0.238890	+	0.125379i
$197$	−1.48310	+	12.2145i	−0.105667	+	0.870244i	0.839433	+	0.543463i	$0.182887\pi$
$197$	−1.48310	+	12.2145i	−0.105667	+	0.870244i	−0.945100	+	0.326781i	$0.894036\pi$
$198$	0.129950	−	1.07023i	0.00923514	−	0.0760582i
$199$	13.5943	+	7.13485i	0.963676	+	0.505776i	0.871729	−	0.489988i	$-0.162999\pi$
$199$	13.5943	+	7.13485i	0.963676	+	0.505776i	0.0919468	+	0.995764i	$0.470691\pi$
$200$	−1.34166	+	1.94374i	−0.0948700	+	0.137443i
$201$	−7.70633	−	4.04460i	−0.543563	−	0.285284i
$202$	−5.95613	+	5.27667i	−0.419072	+	0.371265i
$203$	7.37981	+	19.4590i	0.517961	+	1.36575i
$204$	0.575629	+	4.74073i	0.0403021	+	0.331917i
$205$	−5.25629	−	7.61505i	−0.367115	−	0.531858i
$206$	−1.05646	−	8.70071i	−0.0736069	−	0.606207i
$207$	−1.18624	−	1.05091i	−0.0824491	−	0.0730435i
$208$	3.85733	−	3.41730i	0.267458	−	0.236947i
$209$	4.75914	−	39.1950i	0.329197	−	2.71118i
$210$	7.88386	−	4.13777i	0.544038	−	0.285533i
$211$	8.81469	+	23.2424i	0.606828	+	1.60007i	0.787352	+	0.616504i	$0.211452\pi$
$211$	8.81469	+	23.2424i	0.606828	+	1.60007i	−0.180523	+	0.983571i	$0.557779\pi$
$212$	−2.36483	−	3.42605i	−0.162417	−	0.235302i
$213$	17.9047			1.22681
$214$	7.16337			0.489678
$215$	−4.20766	−	6.09585i	−0.286960	−	0.415733i
$216$	−4.01425	−	3.55631i	−0.273135	−	0.241976i
$217$	−6.54400	−	1.61295i	−0.444236	−	0.109494i
$218$	−1.12942	+	1.63624i	−0.0764938	+	0.110820i
$219$	−6.73166	+	9.75249i	−0.454883	+	0.659012i
$220$	8.03044	−	1.97933i	0.541412	−	0.133446i
$221$	13.0500	−	6.84918i	0.877839	−	0.460725i
$222$	−3.62350	+	3.21015i	−0.243194	+	0.215451i
$223$	−7.06630	−	1.74169i	−0.473194	−	0.116632i	−0.00449540	−	0.999990i	$-0.501431\pi$
$223$	−7.06630	−	1.74169i	−0.473194	−	0.116632i	−0.468699	+	0.883358i	$0.655277\pi$
$224$	3.18746	−	0.785638i	0.212971	−	0.0524926i
$225$	0.0602738	−	0.496399i	0.00401825	−	0.0330933i
$226$	10.1139	−	5.30820i	0.672769	−	0.353096i
$227$	−1.31783	+	3.47482i	−0.0874672	+	0.230632i	−0.971612	−	0.236582i	$-0.923973\pi$
$227$	−1.31783	+	3.47482i	−0.0874672	+	0.230632i	0.884144	+	0.467214i	$0.154742\pi$
$228$	−9.69130	−	8.58574i	−0.641822	−	0.568605i
$229$	4.84348	+	12.7712i	0.320066	+	0.843945i	0.994416	+	0.105533i	$0.0336548\pi$
$229$	4.84348	+	12.7712i	0.320066	+	0.843945i	−0.674350	+	0.738412i	$0.735576\pi$
$230$	4.31128	−	11.3679i	0.284278	−	0.749579i
$231$	27.1023	+	6.68012i	1.78320	+	0.439519i
$232$	5.61328	+	2.94607i	0.368530	+	0.193419i
$233$	11.4462	−	2.82123i	0.749863	−	0.184825i	0.154179	−	0.988043i	$-0.450727\pi$
$233$	11.4462	−	2.82123i	0.749863	−	0.184825i	0.595685	+	0.803218i	$0.296881\pi$
$234$	−0.386899	+	1.02017i	−0.0252924	+	0.0666905i
$235$	0.781438	+	6.43572i	0.0509754	+	0.419820i
$236$	−7.48084			−0.486961
$237$	12.8438	−	7.43718i	0.834292	−	0.483097i
$238$	9.38871			0.608580
$239$	2.06649	+	17.0191i	0.133670	+	1.10088i	0.892964	+	0.450127i	$0.148621\pi$
$239$	2.06649	+	17.0191i	0.133670	+	1.10088i	−0.759294	+	0.650748i	$0.774456\pi$
$240$	0.961757	−	2.53595i	0.0620812	−	0.163695i
$241$	−12.5387	+	3.09052i	−0.807691	+	0.199078i	−0.621478	−	0.783431i	$-0.713468\pi$
$241$	−12.5387	+	3.09052i	−0.807691	+	0.199078i	−0.186213	+	0.982509i	$0.559621\pi$
$242$	13.2190	+	6.93789i	0.849752	+	0.445984i
$243$	2.13224	+	0.525551i	0.136783	+	0.0337141i
$244$	−3.18667	+	8.40256i	−0.204006	+	0.537919i
$245$	−2.17549	−	5.73629i	−0.138987	−	0.366478i
$246$	−7.12025	−	6.30799i	−0.453971	−	0.402183i
$247$	−14.1693	+	37.3615i	−0.901573	+	2.37725i
$248$	−1.81788	+	0.954099i	−0.115436	+	0.0605853i
$249$	2.74287	−	22.5895i	0.173822	−	1.43155i
$250$	11.6100	−	2.86160i	0.734278	−	0.180983i
$251$	−25.0155	−	6.16578i	−1.57897	−	0.389180i	−0.650176	−	0.759784i	$-0.725305\pi$
$251$	−25.0155	−	6.16578i	−1.57897	−	0.389180i	−0.928791	+	0.370604i	$0.879151\pi$
$252$	−0.520251	+	0.460902i	−0.0327727	+	0.0290341i
$253$	33.7497	−	17.7132i	2.12183	−	1.11362i
$254$	2.12111	−	0.522807i	0.133090	−	0.0328039i
$255$	4.40629	−	6.38362i	0.275933	−	0.399758i
$256$	0.568065	−	0.822984i	0.0355040	−	0.0514365i
$257$	17.6492	+	4.35014i	1.10093	+	0.271354i	0.747603	−	0.664146i	$-0.231205\pi$
$257$	17.6492	+	4.35014i	1.10093	+	0.271354i	0.353325	+	0.935501i	$0.385051\pi$
$258$	−5.69976	−	5.04955i	−0.354851	−	0.314371i
$259$	5.40644	+	7.83259i	0.335940	+	0.486693i
$260$	−8.37031			−0.519105
$261$	−1.34219			−0.0830792
$262$	−0.516921	−	0.748889i	−0.0319355	−	0.0462665i
$263$	3.64162	+	9.60216i	0.224552	+	0.592095i	0.999187	−	0.0403138i	$-0.0128357\pi$
$263$	3.64162	+	9.60216i	0.224552	+	0.592095i	−0.774635	+	0.632408i	$0.782067\pi$
$264$	7.52885	−	3.95145i	0.463369	−	0.243195i
$265$	−0.815030	+	6.71238i	−0.0500669	+	0.412338i
$266$	−19.0531	+	16.8795i	−1.16822	+	1.03495i
$267$	1.97706	+	1.75152i	0.120994	+	0.107192i
$268$	0.628249	+	5.17410i	0.0383764	+	0.316058i
$269$	−5.66921	−	8.21327i	−0.345658	−	0.500772i	0.611141	−	0.791522i	$-0.290711\pi$
$269$	−5.66921	−	8.21327i	−0.345658	−	0.500772i	−0.956799	+	0.290750i	$0.906095\pi$
$270$	1.04997	+	8.64730i	0.0638993	+	0.526258i
$271$	3.02972	+	7.98873i	0.184043	+	0.485281i	0.995006	−	0.0998166i	$-0.0318256\pi$
$271$	3.02972	+	7.98873i	0.184043	+	0.485281i	−0.810963	+	0.585097i	$0.801056\pi$
$272$	2.14069	−	1.89648i	0.129798	−	0.114991i
$273$	−25.0136	−	13.1281i	−1.51389	−	0.794550i
$274$	10.2795	−	14.8924i	0.621007	−	0.899683i
$275$	10.6489	+	5.58900i	0.642155	+	0.337029i
$276$	1.50660	−	12.4079i	0.0906864	−	0.746870i
$277$	−1.74088	+	14.3374i	−0.104599	+	0.861453i	0.842097	+	0.539326i	$0.181321\pi$
$277$	−1.74088	+	14.3374i	−0.104599	+	0.861453i	−0.946697	+	0.322127i	$0.895602\pi$
$278$	14.4872	+	7.60349i	0.868886	+	0.456027i
$279$	0.246922	−	0.357729i	0.0147829	−	0.0214167i
$280$	−4.72140	−	2.47798i	−0.282158	−	0.148088i
$281$	0.0877237	−	0.0777164i	0.00523316	−	0.00463617i	−0.660502	−	0.750824i	$-0.729657\pi$
$281$	0.0877237	−	0.0777164i	0.00523316	−	0.00463617i	0.665735	+	0.746188i	$0.268118\pi$
$282$	2.36339	+	6.23175i	0.140738	+	0.371095i
$283$	−2.82377	−	23.2558i	−0.167856	−	1.38242i	−0.796460	−	0.604691i	$-0.793297\pi$
$283$	−2.82377	−	23.2558i	−0.167856	−	1.38242i	0.628605	−	0.777725i	$-0.283626\pi$
$284$	−6.09110	−	8.82448i	−0.361440	−	0.523636i
$285$	2.53487	+	20.8765i	0.150153	+	1.23662i
$286$	−19.6418	−	17.4011i	−1.16144	−	1.02895i
$287$	−13.9984	+	12.4015i	−0.826299	+	0.732037i
$288$	−0.0255201	+	0.210177i	−0.00150379	+	0.0123848i
$289$	−7.81045	+	4.09924i	−0.459438	+	0.241132i
$290$	−3.65129	−	9.62767i	−0.214411	−	0.565356i
$291$	2.95691	+	4.28382i	0.173337	+	0.251122i
$292$	7.09669			0.415302
$293$	5.21102			0.304431			0.152216	−	0.988347i	$-0.451359\pi$
$293$	5.21102			0.304431			0.152216	+	0.988347i	$0.451359\pi$
$294$	−3.58283	−	5.19062i	−0.208955	−	0.302723i
$295$	9.09496	+	8.05743i	0.529529	+	0.469122i
$296$	2.81485	+	0.693799i	0.163610	+	0.0403263i
$297$	−15.5131	+	22.4745i	−0.900159	+	1.30411i
$298$	1.38135	−	2.00123i	0.0800196	−	0.115928i
$299$	−37.4534	+	9.23144i	−2.16599	+	0.533868i
$300$	3.49205	−	1.83277i	0.201614	−	0.105815i
$301$	−11.2057	+	9.92740i	−0.645887	+	0.572206i
$302$	17.1080	+	4.21674i	0.984454	+	0.242646i
$303$	12.9011	−	3.17984i	0.741150	−	0.182677i
$304$	−0.934620	+	7.69729i	−0.0536041	+	0.441470i
$305$	12.9244	−	6.78327i	0.740052	−	0.388409i
$306$	−0.214715	+	0.566158i	−0.0122745	+	0.0323651i
$307$	15.5886	+	13.8103i	0.889686	+	0.788193i	0.978153	−	0.207886i	$-0.0666585\pi$
$307$	15.5886	+	13.8103i	0.889686	+	0.788193i	−0.0884674	+	0.996079i	$0.528197\pi$
$308$	−5.92774	−	15.6302i	−0.337765	−	0.890612i
$309$	−5.18974	+	13.6842i	−0.295234	+	0.778468i
$310$	3.23776	+	0.798037i	0.183892	+	0.0453254i
$311$	−22.6025	−	11.8627i	−1.28167	−	0.672673i	−0.320141	−	0.947370i	$-0.603730\pi$
$311$	−22.6025	−	11.8627i	−1.28167	−	0.672673i	−0.961531	+	0.274696i	$0.911423\pi$
$312$	−8.35508	+	2.05934i	−0.473013	+	0.116587i
$313$	11.7979	−	31.1085i	0.666857	−	1.75836i	0.0151512	−	0.999885i	$-0.495177\pi$
$313$	11.7979	−	31.1085i	0.666857	−	1.75836i	0.651706	−	0.758472i	$-0.274054\pi$
$314$	−0.209264	−	1.72344i	−0.0118095	−	0.0972596i
$315$	1.12893			0.0636080
$316$	−8.03489	−	3.80007i	−0.451998	−	0.213771i
$317$	−25.7292			−1.44510			−0.722549	−	0.691320i	$-0.757029\pi$
$317$	−25.7292			−1.44510			−0.722549	+	0.691320i	$0.757029\pi$
$318$	0.837894	+	6.90068i	0.0469868	+	0.386971i
$319$	11.4469	−	30.1830i	0.640903	−	1.68992i
$320$	−1.57705	+	0.388708i	−0.0881598	+	0.0217295i
$321$	−10.5914	−	5.55879i	−0.591153	−	0.310261i
$322$	−23.8591	−	5.88074i	−1.32961	−	0.327721i
$323$	−7.86349	+	20.7343i	−0.437536	+	1.15369i
$324$	2.95032	+	7.77935i	0.163906	+	0.432186i
$325$	−9.11031	−	8.07103i	−0.505349	−	0.447700i
$326$	−5.26514	+	13.8830i	−0.291609	+	0.768910i
$327$	2.93963	−	1.54283i	0.162562	−	0.0853189i
$328$	−0.686670	+	5.65524i	−0.0379150	+	0.312258i
$329$	12.7223	−	3.13577i	0.701405	−	0.172881i
$330$	−13.4093	−	3.30511i	−0.738160	−	0.181940i
$331$	25.1055	−	22.2416i	1.37992	−	1.22251i	0.432861	−	0.901461i	$-0.357504\pi$
$331$	25.1055	−	22.2416i	1.37992	−	1.22251i	0.947064	−	0.321046i	$-0.104034\pi$
$332$	−12.0666	+	6.33303i	−0.662240	+	0.347570i
$333$	−0.595963	+	0.146892i	−0.0326586	+	0.00804961i
$334$	3.62940	−	5.25810i	0.198592	−	0.287710i
$335$	4.80909	−	6.96717i	0.262749	−	0.380657i
$336$	−5.32246	−	1.31187i	−0.290364	−	0.0715683i
$337$	7.58963	+	6.72382i	0.413433	+	0.366270i	0.844050	−	0.536265i	$-0.180165\pi$
$337$	7.58963	+	6.72382i	0.413433	+	0.366270i	−0.430616	+	0.902535i	$0.641704\pi$
$338$	7.70122	+	11.1571i	0.418891	+	0.606869i
$339$	−19.0731			−1.03591
$340$	−4.64523			−0.251923
$341$	5.93869	+	8.60367i	0.321598	+	0.465915i
$342$	−0.582135	−	1.53496i	−0.0314783	−	0.0830014i
$343$	9.36836	−	4.91689i	0.505844	−	0.265487i
$344$	−0.549679	+	4.52702i	−0.0296367	+	0.244080i
$345$	−15.1960	+	13.4624i	−0.818123	+	0.724794i
$346$	8.55261	+	7.57695i	0.459791	+	0.407339i
$347$	1.50815	+	12.4207i	0.0809615	+	0.666778i	0.975533	+	0.219853i	$0.0705578\pi$
$347$	1.50815	+	12.4207i	0.0809615	+	0.666778i	−0.894572	+	0.446925i	$0.852519\pi$
$348$	−6.01333	−	8.71182i	−0.322349	−	0.467003i
$349$	2.43940	+	20.0902i	0.130578	+	1.07541i	0.899763	+	0.436380i	$0.143740\pi$
$349$	2.43940	+	20.0902i	0.130578	+	1.07541i	−0.769185	+	0.639027i	$0.779337\pi$
$350$	−2.74942	−	7.24964i	−0.146963	−	0.387509i
$351$	20.6868	−	18.3269i	1.10418	−	0.978217i
$352$	−4.50880	−	2.36640i	−0.240320	−	0.126129i
$353$	7.25044	−	10.5041i	0.385902	−	0.559075i	−0.581104	−	0.813829i	$-0.697379\pi$
$353$	7.25044	−	10.5041i	0.385902	−	0.559075i	0.967006	+	0.254754i	$0.0819944\pi$
$354$	11.0608	+	5.80514i	0.587873	+	0.308540i
$355$	−2.09928	+	17.2891i	−0.111418	+	0.917610i
$356$	0.190666	−	1.57028i	0.0101053	−	0.0832245i
$357$	−13.8817	−	7.28565i	−0.734695	−	0.385598i
$358$	−2.85291	+	4.13316i	−0.150781	+	0.218444i
$359$	9.05023	+	4.74993i	0.477653	+	0.250692i	0.686326	−	0.727294i	$-0.259222\pi$
$359$	9.05023	+	4.74993i	0.477653	+	0.250692i	−0.208673	+	0.977985i	$0.566915\pi$
$360$	0.257403	−	0.228039i	0.0135663	−	0.0120187i
$361$	−14.5820	−	38.4495i	−0.767472	−	2.02366i
$362$	−2.99562	−	24.6711i	−0.157446	−	1.29669i
$363$	−14.1612	−	20.5160i	−0.743268	−	1.07681i
$364$	2.03920	+	16.7943i	0.106883	+	0.880261i
$365$	−8.62793	−	7.64368i	−0.451606	−	0.400088i
$366$	11.2320	−	9.95072i	0.587108	−	0.520132i
$367$	0.641192	−	5.28069i	0.0334699	−	0.275650i	−0.966360	−	0.257194i	$-0.917202\pi$
$367$	0.641192	−	5.28069i	0.0334699	−	0.275650i	0.999830	−	0.0184556i	$-0.00587492\pi$
$368$	−6.62791	+	3.47859i	−0.345504	+	0.181334i
$369$	−0.427698	−	1.12775i	−0.0222651	−	0.0587082i
$370$	−2.67493	−	3.87531i	−0.139063	−	0.201468i
$371$	13.6664			0.709522
$372$	3.42821			0.177744
$373$	8.54116	+	12.3740i	0.442245	+	0.640702i	0.979197	−	0.202910i	$-0.0650400\pi$
$373$	8.54116	+	12.3740i	0.442245	+	0.640702i	−0.536953	+	0.843612i	$0.680425\pi$
$374$	−10.9005	−	9.65700i	−0.563652	−	0.499352i
$375$	−19.3865	−	4.77834i	−1.00111	−	0.246752i
$376$	2.26736	−	3.28484i	0.116930	−	0.169403i
$377$	−18.5582	+	26.8862i	−0.955797	+	1.38471i
$378$	17.0943	−	4.21336i	0.879234	−	0.216712i
$379$	−15.5673	+	8.17036i	−0.799639	+	0.419683i	−0.814469	−	0.580207i	$-0.802972\pi$
$379$	−15.5673	+	8.17036i	−0.799639	+	0.419683i	0.0148299	+	0.999890i	$0.495279\pi$
$380$	9.42685	−	8.35146i	0.483587	−	0.428421i
$381$	−3.54187	−	0.872991i	−0.181455	−	0.0447247i
$382$	18.6549	−	4.59801i	0.954466	−	0.235255i
$383$	−1.06285	+	8.75333i	−0.0543089	+	0.447274i	0.940036	+	0.341075i	$0.110791\pi$
$383$	−1.06285	+	8.75333i	−0.0543089	+	0.447274i	−0.994345	+	0.106199i	$0.966132\pi$
$384$	−1.47855	+	0.776001i	−0.0754518	+	0.0396002i
$385$	−9.62813	+	25.3873i	−0.490695	+	1.29386i
$386$	−1.95629	−	1.73312i	−0.0995725	−	0.0882136i
$387$	−0.342372	−	0.902761i	−0.0174038	−	0.0458899i
$388$	1.10539	−	2.91468i	0.0561178	−	0.147971i
$389$	7.41817	+	1.82842i	0.376116	+	0.0927044i	0.422842	−	0.906203i	$-0.361033\pi$
$389$	7.41817	+	1.82842i	0.376116	+	0.0927044i	−0.0467257	+	0.998908i	$0.514879\pi$
$390$	12.3759	+	6.49537i	0.626678	+	0.328906i
$391$	−20.7854	+	5.12313i	−1.05116	+	0.259088i
$392$	−1.33938	+	3.53166i	−0.0676490	+	0.178376i
$393$	0.183153	+	1.50840i	0.00923883	+	0.0760886i
$394$	−12.3042			−0.619875
$395$	5.67560	+	13.2742i	0.285570	+	0.667897i
$396$	1.07809			0.0541763
$397$	4.34054	+	35.7475i	0.217845	+	1.79412i	0.534077	+	0.845436i	$0.320659\pi$
$397$	4.34054	+	35.7475i	0.217845	+	1.79412i	−0.316232	+	0.948682i	$0.602418\pi$
$398$	−5.44422	+	14.3552i	−0.272894	+	0.719562i
$399$	41.2694	−	10.1720i	2.06605	−	0.509237i
$400$	−2.09128	−	1.09759i	−0.104564	−	0.0548795i
$401$	−22.5197	−	5.55060i	−1.12458	−	0.277184i	−0.367189	−	0.930146i	$-0.619680\pi$
$401$	−22.5197	−	5.55060i	−1.12458	−	0.277184i	−0.757390	+	0.652963i	$0.773526\pi$
$402$	3.08621	−	8.13767i	0.153926	−	0.405870i
$403$	−3.75174	−	9.89253i	−0.186888	−	0.492782i
$404$	−5.95613	−	5.27667i	−0.296328	−	0.262524i
$405$	4.79205	−	12.6356i	0.238119	−	0.627868i
$406$	−18.4275	+	9.67152i	−0.914544	+	0.479990i
$407$	1.77941	−	14.6547i	0.0882020	−	0.726409i
$408$	−4.63678	+	1.14286i	−0.229555	+	0.0565802i
$409$	22.4440	+	5.53194i	1.10978	+	0.273537i	0.751275	−	0.659990i	$-0.229439\pi$
$409$	22.4440	+	5.53194i	1.10978	+	0.273537i	0.358508	+	0.933527i	$0.383285\pi$
$410$	6.92596	−	6.13586i	0.342049	−	0.303029i
$411$	−26.7552	+	14.0422i	−1.31974	+	0.692652i
$412$	8.50993	−	2.09751i	0.419254	−	0.103337i
$413$	13.9508	−	20.2112i	0.686474	−	0.994530i
$414$	0.900266	−	1.30426i	0.0442456	−	0.0641009i
$415$	21.4913	+	5.29713i	1.05497	+	0.260026i
$416$	3.85733	+	3.41730i	0.189121	+	0.167547i
$417$	−15.5197	−	22.4842i	−0.760005	−	1.10106i
$418$	39.4829			1.93117
$419$	−16.3673			−0.799593			−0.399796	−	0.916604i	$-0.630919\pi$
$419$	−16.3673			−0.799593			−0.399796	+	0.916604i	$0.630919\pi$
$420$	5.05789	+	7.32762i	0.246800	+	0.357551i
$421$	2.50398	+	6.60246i	0.122037	+	0.321784i	0.982088	−	0.188423i	$-0.0603377\pi$
$421$	2.50398	+	6.60246i	0.122037	+	0.321784i	−0.860051	+	0.510208i	$0.829569\pi$
$422$	−22.0105	+	11.5520i	−1.07145	+	0.562342i
$423$	−0.101860	+	0.838895i	−0.00495262	+	0.0407885i
$424$	3.11602	−	2.76055i	0.151327	−	0.134064i
$425$	−5.05591	−	4.47914i	−0.245247	−	0.217270i
$426$	2.15817	+	17.7741i	0.104564	+	0.861158i
$427$	−16.7587	−	24.2792i	−0.811012	−	1.17495i
$428$	0.863449	+	7.11114i	0.0417364	+	0.343730i
$429$	15.5380	+	40.9704i	0.750182	+	1.97807i
$430$	5.54423	−	4.91176i	0.267366	−	0.236866i
$431$	−2.88005	−	1.51156i	−0.138727	−	0.0728095i	0.393932	−	0.919140i	$-0.371115\pi$
$431$	−2.88005	−	1.51156i	−0.138727	−	0.0728095i	−0.532659	+	0.846330i	$0.678807\pi$
$432$	3.04652	−	4.41364i	0.146576	−	0.212352i
$433$	−8.09755	−	4.24992i	−0.389143	−	0.204238i	0.258793	−	0.965933i	$-0.416675\pi$
$433$	−8.09755	−	4.24992i	−0.389143	−	0.204238i	−0.647936	+	0.761695i	$0.724368\pi$
$434$	0.812399	−	6.69071i	0.0389964	−	0.321164i
$435$	−2.07248	+	17.0684i	−0.0993676	+	0.818366i
$436$	−1.76045	−	0.923956i	−0.0843103	−	0.0442495i
$437$	32.9703	−	47.7657i	1.57718	−	2.28494i
$438$	−10.4928	−	5.50704i	−0.501365	−	0.263137i
$439$	17.4275	−	15.4394i	0.831769	−	0.736883i	−0.135462	−	0.990783i	$-0.543252\pi$
$439$	17.4275	−	15.4394i	0.831769	−	0.736883i	0.967231	+	0.253900i	$0.0817133\pi$
$440$	2.93286	+	7.73331i	0.139818	+	0.368671i
$441$	−0.0963923	−	0.793862i	−0.00459011	−	0.0378030i
$442$	8.37224	+	12.1293i	0.398227	+	0.576931i
$443$	−0.458637	−	3.77721i	−0.0217905	−	0.179461i	0.977750	−	0.209774i	$-0.0672727\pi$
$443$	−0.458637	−	3.77721i	−0.0217905	−	0.179461i	−0.999540	+	0.0303128i	$0.990350\pi$
$444$	−3.62350	−	3.21015i	−0.171964	−	0.152347i
$445$	−1.92311	+	1.70373i	−0.0911643	+	0.0807645i
$446$	0.877239	−	7.22471i	0.0415385	−	0.342100i
$447$	−3.59536	+	1.88699i	−0.170054	+	0.0892515i
$448$	1.16412	+	3.06952i	0.0549993	+	0.145021i
$449$	−9.24927	−	13.3999i	−0.436500	−	0.632380i	0.541570	−	0.840656i	$-0.317830\pi$
$449$	−9.24927	−	13.3999i	−0.436500	−	0.632380i	−0.978070	+	0.208276i	$0.933215\pi$
$450$	0.500045			0.0235724
$451$	29.0083			1.36595
$452$	6.48860	+	9.40035i	0.305198	+	0.442155i
$453$	−22.0228	−	19.5105i	−1.03472	−	0.916682i
$454$	−3.60833	−	0.889374i	−0.169347	−	0.0417404i
$455$	15.6096	−	22.6144i	0.731787	−	1.06018i
$456$	7.35498	−	10.6555i	0.344429	−	0.498991i
$457$	13.4210	−	3.30798i	0.627809	−	0.154741i	0.0874406	−	0.996170i	$-0.472131\pi$
$457$	13.4210	−	3.30798i	0.627809	−	0.154741i	0.540368	+	0.841429i	$0.318285\pi$
$458$	−12.0943	+	6.34756i	−0.565128	+	0.296602i
$459$	11.4805	−	10.1708i	0.535862	−	0.474732i
$460$	11.8047	+	2.90960i	0.550397	+	0.135661i
$461$	6.36483	−	1.56879i	0.296440	−	0.0730659i	−0.0882908	−	0.996095i	$-0.528140\pi$
$461$	6.36483	−	1.56879i	0.296440	−	0.0730659i	0.384731	+	0.923029i	$0.374294\pi$
$462$	−3.36459	+	27.7099i	−0.156535	+	1.28918i
$463$	−4.86815	+	2.55500i	−0.226242	+	0.118741i	−0.574036	−	0.818830i	$-0.694623\pi$
$463$	−4.86815	+	2.55500i	−0.226242	+	0.118741i	0.347794	+	0.937571i	$0.386931\pi$
$464$	−2.24799	+	5.92746i	−0.104360	+	0.275175i
$465$	−4.16790	−	3.69244i	−0.193282	−	0.171233i
$466$	4.18034	+	11.0226i	0.193650	+	0.510614i
$467$	−4.44729	+	11.7266i	−0.205796	+	0.542640i	−0.997683	−	0.0680273i	$-0.978329\pi$
$467$	−4.44729	+	11.7266i	−0.205796	+	0.542640i	0.791887	+	0.610667i	$0.209099\pi$
$468$	−1.05937	−	0.261110i	−0.0489692	−	0.0120698i
$469$	−15.1506	−	7.95167i	−0.699591	−	0.367174i
$470$	−6.29460	+	1.55148i	−0.290348	+	0.0715644i
$471$	−1.02799	+	2.71058i	−0.0473672	+	0.124897i
$472$	−0.901715	−	7.42630i	−0.0415048	−	0.341823i
$473$	23.2212			1.06771
$474$	8.93110	+	11.8537i	0.410219	+	0.544457i
$475$	18.3131			0.840262
$476$	1.13168	+	9.32026i	0.0518707	+	0.427193i
$477$	−0.312543	+	0.824108i	−0.0143104	+	0.0377333i
$478$	−16.6459	+	4.10286i	−0.761368	+	0.187660i
$479$	6.75949	+	3.54766i	0.308849	+	0.162097i	0.612026	−	0.790838i	$-0.290355\pi$
$479$	6.75949	+	3.54766i	0.308849	+	0.162097i	−0.303177	+	0.952934i	$0.598047\pi$
$480$	2.63338	+	0.649070i	0.120197	+	0.0296259i
$481$	−5.29781	+	13.9692i	−0.241559	+	0.636940i
$482$	−4.57937	−	12.0748i	−0.208584	−	0.549992i
$483$	30.7133	+	27.2096i	1.39750	+	1.23808i
$484$	−5.29392	+	13.9589i	−0.240633	+	0.634497i
$485$	−4.48324	+	2.35298i	−0.203573	+	0.106844i
$486$	−0.264705	+	2.18004i	−0.0120073	+	0.0988888i
$487$	2.92448	−	0.720818i	0.132521	−	0.0326634i	−0.172497	−	0.985010i	$-0.555184\pi$
$487$	2.92448	−	0.720818i	0.132521	−	0.0326634i	0.305018	+	0.952347i	$0.401337\pi$
$488$	−8.72540	−	2.15062i	−0.394981	−	0.0973540i
$489$	18.5580	−	16.4410i	0.839222	−	0.743486i
$490$	5.43224	−	2.85106i	0.245404	−	0.128798i
$491$	12.2060	−	3.00851i	0.550850	−	0.135772i	0.0459398	−	0.998944i	$-0.485372\pi$
$491$	12.2060	−	3.00851i	0.550850	−	0.135772i	0.504910	+	0.863172i	$0.331526\pi$
$492$	5.40375	−	7.82868i	0.243620	−	0.352944i
$493$	−10.2992	+	14.9209i	−0.463851	+	0.672005i
$494$	−38.7970	−	9.56260i	−1.74556	−	0.430242i
$495$	−1.31071	−	1.16119i	−0.0589122	−	0.0521916i
$496$	−1.16626	−	1.68963i	−0.0523668	−	0.0758664i
$497$	35.2005			1.57896
$498$	22.7554			1.01970
$499$	−17.9276	−	25.9726i	−0.802548	−	1.16269i	−0.983803	−	0.179255i	$-0.942631\pi$
$499$	−17.9276	−	25.9726i	−0.802548	−	1.16269i	0.181255	−	0.983436i	$-0.441984\pi$
$500$	4.24016	+	11.1804i	0.189626	+	0.500002i
$501$	−9.44653	+	4.95792i	−0.422040	+	0.221504i
$502$	3.10553	−	25.5763i	0.138607	−	1.14153i
$503$	−12.0353	+	10.6624i	−0.536629	+	0.475411i	−0.887368	−	0.461062i	$-0.847469\pi$
$503$	−12.0353	+	10.6624i	−0.536629	+	0.475411i	0.350740	+	0.936473i	$0.385930\pi$
$504$	−0.520251	−	0.460902i	−0.0231738	−	0.0205302i
$505$	1.55789	+	12.8304i	0.0693253	+	0.570946i
$506$	21.6521	+	31.3685i	0.962555	+	1.39450i
$507$	−2.72866	−	22.4725i	−0.121184	−	0.998040i
$508$	0.774668	+	2.04263i	0.0343703	+	0.0906271i
$509$	6.64570	−	5.88758i	0.294566	−	0.260962i	−0.502876	−	0.864359i	$-0.667725\pi$
$509$	6.64570	−	5.88758i	0.294566	−	0.260962i	0.797442	+	0.603396i	$0.206186\pi$
$510$	6.86820	+	3.60471i	0.304129	+	0.159619i
$511$	−13.2344	+	19.1734i	−0.585456	+	0.848180i
$512$	0.885456	+	0.464723i	0.0391320	+	0.0205381i
$513$	−5.01234	+	41.2804i	−0.221300	+	1.82257i
$514$	−2.19105	+	18.0449i	−0.0966429	+	0.795926i
$515$	−12.6053	−	6.61576i	−0.555455	−	0.291525i
$516$	4.32570	−	6.26686i	0.190428	−	0.275883i
$517$	−17.9963	−	9.44518i	−0.791476	−	0.415399i
$518$	−7.12380	+	6.31114i	−0.313002	+	0.277296i
$519$	−6.76571	−	17.8397i	−0.296982	−	0.783076i
$520$	−1.00893	−	8.30928i	−0.0442445	−	0.364386i
$521$	5.70489	+	8.26496i	0.249936	+	0.362094i	0.927791	−	0.373101i	$-0.121706\pi$
$521$	5.70489	+	8.26496i	0.249936	+	0.362094i	−0.677855	+	0.735196i	$0.737090\pi$
$522$	−0.161783	−	1.33240i	−0.00708104	−	0.0583176i
$523$	−7.28374	−	6.45283i	−0.318496	−	0.282163i	0.488693	−	0.872456i	$-0.337474\pi$
$523$	−7.28374	−	6.45283i	−0.318496	−	0.282163i	−0.807189	+	0.590293i	$0.799012\pi$
$524$	0.681121	−	0.603420i	0.0297549	−	0.0263605i
$525$	−1.56057	+	12.8525i	−0.0681090	+	0.560928i
$526$	−9.09320	+	4.77248i	−0.396482	+	0.208090i
$527$	−2.08209	−	5.49001i	−0.0906971	−	0.239149i
$528$	4.83014	+	6.99766i	0.210205	+	0.304534i
$529$	33.0298			1.43608
$530$	−6.76168			−0.293708
$531$	0.899729	+	1.30348i	0.0390449	+	0.0565663i
$532$	−19.0531	−	16.8795i	−0.826055	−	0.731821i
$533$	−28.5044	−	7.02569i	−1.23466	−	0.304317i
$534$	−1.50045	+	2.17377i	−0.0649306	+	0.0940682i
$535$	6.60949	−	9.57550i	0.285753	−	0.413985i
$536$	−5.06065	+	1.24734i	−0.218587	+	0.0538768i
$537$	7.42550	−	3.89720i	0.320434	−	0.168177i
$538$	7.47004	−	6.61788i	0.322056	−	0.285317i
$539$	18.6744	+	4.60282i	0.804363	+	0.198258i
$540$	−8.45769	+	2.08463i	−0.363961	+	0.0897083i
$541$	−4.70355	+	38.7372i	−0.202221	+	1.66544i	0.439302	+	0.898339i	$0.355226\pi$
$541$	−4.70355	+	38.7372i	−0.202221	+	1.66544i	−0.641524	+	0.767103i	$0.721697\pi$
$542$	−7.56529	+	3.97057i	−0.324957	+	0.170551i
$543$	−14.7157	+	38.8020i	−0.631510	+	1.66515i
$544$	2.14069	+	1.89648i	0.0917812	+	0.0813110i
$545$	1.14513	+	3.01945i	0.0490519	+	0.129339i
$546$	10.0174	−	26.4136i	0.428703	−	1.13040i
$547$	−14.5164	−	3.57798i	−0.620678	−	0.152983i	−0.0835767	−	0.996501i	$-0.526634\pi$
$547$	−14.5164	−	3.57798i	−0.620678	−	0.152983i	−0.537101	+	0.843518i	$0.680481\pi$
$548$	16.0229	+	8.40946i	0.684464	+	0.359234i
$549$	1.84735	−	0.455331i	0.0788429	−	0.0194330i
$550$	−4.26466	+	11.2450i	−0.181846	+	0.479488i
$551$	−5.92495	−	48.7963i	−0.252411	−	2.07879i
$552$	12.4991			0.531996
$553$	25.2508	−	14.6215i	1.07377	−	0.621769i
$554$	−14.4427			−0.613613
$555$	0.947769	+	7.80558i	0.0402306	+	0.331329i
$556$	−5.80181	+	15.2981i	−0.246051	+	0.648784i
$557$	27.8275	−	6.85886i	1.17909	−	0.290619i	0.399394	−	0.916779i	$-0.369220\pi$
$557$	27.8275	−	6.85886i	1.17909	−	0.290619i	0.779695	+	0.626160i	$0.215374\pi$
$558$	0.384884	+	0.202003i	0.0162934	+	0.00855145i
$559$	−22.8177	−	5.62407i	−0.965087	−	0.237873i
$560$	1.89081	−	4.98566i	0.0799014	−	0.210683i
$561$	8.62306	+	22.7371i	0.364066	+	0.959963i
$562$	0.0877237	+	0.0777164i	0.00370040	+	0.00327827i
$563$	7.06210	−	18.6212i	0.297632	−	0.784791i	−0.699878	−	0.714263i	$-0.746762\pi$
$563$	7.06210	−	18.6212i	0.297632	−	0.784791i	0.997510	−	0.0705284i	$-0.0224686\pi$
$564$	−5.90143	+	3.09731i	−0.248495	+	0.130420i
$565$	2.23627	−	18.4174i	0.0940807	−	0.774824i
$566$	22.7459	−	5.60636i	0.956082	−	0.235653i
$567$	−26.5197	−	6.53651i	−1.11372	−	0.274508i
$568$	8.02594	−	7.11036i	0.336761	−	0.298344i
$569$	−24.6165	+	12.9197i	−1.03198	+	0.541624i	−0.893651	−	0.448763i	$-0.851865\pi$
$569$	−24.6165	+	12.9197i	−1.03198	+	0.541624i	−0.138327	+	0.990387i	$0.544173\pi$
$570$	−20.4188	+	5.03278i	−0.855248	+	0.210800i
$571$	4.58240	−	6.63876i	0.191768	−	0.277823i	−0.715292	−	0.698826i	$-0.753706\pi$
$571$	4.58240	−	6.63876i	0.191768	−	0.277823i	0.907060	+	0.421002i	$0.138322\pi$
$572$	14.9067	−	21.5960i	0.623279	−	0.902975i
$573$	−31.1502	−	7.67783i	−1.30132	−	0.320746i
$574$	−13.9984	−	12.4015i	−0.584282	−	0.517628i
$575$	10.0428	+	14.5495i	0.418812	+	0.606754i
$576$	−0.211721			−0.00882170
$577$	−27.8524			−1.15951			−0.579755	−	0.814791i	$-0.696852\pi$
$577$	−27.8524			−1.15951			−0.579755	+	0.814791i	$0.696852\pi$
$578$	−5.01080	−	7.25939i	−0.208422	−	0.301951i
$579$	1.54756	+	4.08059i	0.0643145	+	0.169583i
$580$	9.11736	−	4.78516i	0.378578	−	0.198693i
$581$	5.39247	−	44.4110i	0.223717	−	1.84248i
$582$	−3.89617	+	3.45171i	−0.161502	+	0.143078i
$583$	−15.8669	−	14.0569i	−0.657142	−	0.582177i
$584$	0.855412	+	7.04495i	0.0353972	+	0.291522i
$585$	1.00671	+	1.45847i	0.0416222	+	0.0603002i
$586$	0.628119	+	5.17303i	0.0259474	+	0.213696i
$587$	2.43757	+	6.42734i	0.100609	+	0.265285i	0.975865	−	0.218376i	$-0.0700760\pi$
$587$	2.43757	+	6.42734i	0.100609	+	0.265285i	−0.875255	+	0.483661i	$0.839307\pi$
$588$	4.72091	−	4.18236i	0.194687	−	0.172478i
$589$	14.0955	+	7.39791i	0.580797	+	0.304826i
$590$	−6.90241	+	9.99987i	−0.284168	+	0.411688i
$591$	18.1923	+	9.54805i	0.748331	+	0.392754i
$592$	−0.349447	+	2.87796i	−0.0143622	+	0.118283i
$593$	−0.274822	+	2.26336i	−0.0112856	+	0.0929451i	−0.997263	−	0.0739320i	$-0.976445\pi$
$593$	−0.274822	+	2.26336i	−0.0112856	+	0.0929451i	0.985978	+	0.166877i	$0.0533683\pi$
$594$	−24.1806	−	12.6909i	−0.992141	−	0.520716i
$595$	8.66277	−	12.5502i	0.355139	−	0.514507i
$596$	2.15315	+	1.13006i	0.0881963	+	0.0462890i
$597$	19.1892	−	17.0001i	0.785362	−	0.695770i
$598$	−13.6786	−	36.0676i	−0.559361	−	1.47492i
$599$	5.44789	+	44.8674i	0.222595	+	1.83323i	0.492462	+	0.870334i	$0.336097\pi$
$599$	5.44789	+	44.8674i	0.222595	+	1.83323i	−0.269868	+	0.962897i	$0.586980\pi$
$600$	2.24033	+	3.24568i	0.0914611	+	0.132504i
$601$	−1.77915	−	14.6526i	−0.0725728	−	0.597691i	−0.982945	−	0.183900i	$-0.941128\pi$
$601$	−1.77915	−	14.6526i	−0.0725728	−	0.597691i	0.910372	−	0.413791i	$-0.135795\pi$
$602$	−11.2057	−	9.92740i	−0.456711	−	0.404610i
$603$	0.825989	−	0.731762i	0.0336369	−	0.0297997i
$604$	−2.12386	+	17.4915i	−0.0864184	+	0.711720i
$605$	21.4710	−	11.2689i	0.872921	−	0.458144i
$606$	4.71171	+	12.4238i	0.191400	+	0.504681i
$607$	−0.0442620	−	0.0641245i	−0.00179654	−	0.00260273i	0.822085	−	0.569365i	$-0.192811\pi$
$607$	−0.0442620	−	0.0641245i	−0.00179654	−	0.00260273i	−0.823881	+	0.566763i	$0.808196\pi$
$608$	−7.75382			−0.314459
$609$	34.7511			1.40819
$610$	8.29169	+	12.0126i	0.335721	+	0.486375i
$611$	15.3961	+	13.6397i	0.622858	+	0.551804i
$612$	−0.587911	−	0.144907i	−0.0237649	−	0.00585752i
$613$	4.09255	−	5.92908i	0.165296	−	0.239473i	−0.731579	−	0.681757i	$-0.761216\pi$
$613$	4.09255	−	5.92908i	0.165296	−	0.239473i	0.896875	+	0.442284i	$0.145832\pi$
$614$	−11.8306	+	17.1395i	−0.477443	+	0.691695i
$615$	−15.0018	+	3.69761i	−0.604930	+	0.149102i
$616$	14.8017	−	7.76853i	0.596378	−	0.313003i
$617$	−35.2053	+	31.1892i	−1.41731	+	1.25563i	−0.495160	+	0.868802i	$0.664890\pi$
$617$	−35.2053	+	31.1892i	−1.41731	+	1.25563i	−0.922152	+	0.386827i	$0.873571\pi$
$618$	−14.2100	−	3.50245i	−0.571610	−	0.140889i
$619$	−23.8864	+	5.88748i	−0.960077	+	0.236638i	−0.688059	−	0.725655i	$-0.741537\pi$
$619$	−23.8864	+	5.88748i	−0.960077	+	0.236638i	−0.272018	+	0.962292i	$0.587691\pi$
$620$	−0.401949	+	3.31035i	−0.0161427	+	0.132947i
$621$	−35.5453	+	18.6556i	−1.42638	+	0.748624i
$622$	9.05180	−	23.8676i	0.362944	−	0.957005i
$623$	3.88690	+	3.44349i	0.155725	+	0.137961i
$624$	−3.05142	−	8.04593i	−0.122155	−	0.322095i
$625$	2.69952	−	7.11805i	0.107981	−	0.284722i
$626$	32.3038	+	7.96217i	1.29112	+	0.318232i
$627$	−58.3774	−	30.6388i	−2.33137	−	1.22360i
$628$	1.68565	−	0.415477i	0.0672650	−	0.0165793i
$629$	−2.94010	+	7.75241i	−0.117230	+	0.309109i
$630$	0.136078	+	1.12070i	0.00542146	+	0.0446497i
$631$	−18.2220			−0.725405			−0.362703	−	0.931905i	$-0.618146\pi$
$631$	−18.2220			−0.725405			−0.362703	+	0.931905i	$0.618146\pi$
$632$	2.80386	−	8.43436i	0.111532	−	0.335501i
$633$	41.5079			1.64979
$634$	−3.10131	−	25.5416i	−0.123169	−	1.01439i
$635$	1.25825	−	3.31774i	0.0499323	−	0.131661i
$636$	−6.74937	+	1.66357i	−0.267630	+	0.0659648i
$637$	−17.2352	−	9.04572i	−0.682883	−	0.358404i
$638$	31.3427	+	7.72528i	1.24087	+	0.305847i
$639$	−0.805018	+	2.12266i	−0.0318460	+	0.0839711i
$640$	−0.575967	−	1.51870i	−0.0227671	−	0.0600319i
$641$	7.36293	+	6.52299i	0.290818	+	0.257643i	0.795899	−	0.605430i	$-0.206999\pi$
$641$	7.36293	+	6.52299i	0.290818	+	0.257643i	−0.505080	+	0.863072i	$0.668537\pi$
$642$	4.24161	−	11.1842i	0.167403	−	0.441405i
$643$	−20.9655	+	11.0035i	−0.826799	+	0.433937i	−0.824364	−	0.566060i	$-0.808467\pi$
$643$	−20.9655	+	11.0035i	−0.826799	+	0.433937i	−0.00243444	+	0.999997i	$0.500775\pi$
$644$	2.96196	−	24.3940i	0.116718	−	0.961257i
$645$	−12.0089	+	2.95993i	−0.472851	+	0.116547i
$646$	−21.5310	−	5.30691i	−0.847125	−	0.208798i
$647$	−21.6392	+	19.1706i	−0.850724	+	0.753676i	−0.971004	−	0.239064i	$-0.923159\pi$
$647$	−21.6392	+	19.1706i	−0.850724	+	0.753676i	0.120280	+	0.992740i	$0.461621\pi$
$648$	−7.36700	+	3.86650i	−0.289403	+	0.151891i
$649$	−36.9860	+	9.11622i	−1.45183	+	0.357843i
$650$	6.91405	−	10.0167i	0.271192	−	0.392889i
$651$	−6.39317	+	9.26210i	−0.250568	+	0.363010i
$652$	−14.4165	−	3.55334i	−0.564592	−	0.139159i
$653$	−25.1051	−	22.2412i	−0.982439	−	0.870365i	0.00912855	−	0.999958i	$-0.497094\pi$
$653$	−25.1051	−	22.2412i	−0.982439	−	0.870365i	−0.991567	+	0.129594i	$0.958633\pi$
$654$	1.88592	+	2.73222i	0.0737452	+	0.106838i
$655$	−1.47801			−0.0577508
$656$	−5.69677			−0.222422
$657$	−0.853527	−	1.23655i	−0.0332993	−	0.0482423i
$658$	4.64642	+	12.2516i	0.181136	+	0.477617i
$659$	−9.02042	+	4.73428i	−0.351386	+	0.184421i	−0.631176	−	0.775640i	$-0.717427\pi$
$659$	−9.02042	+	4.73428i	−0.351386	+	0.184421i	0.279790	+	0.960061i	$0.409735\pi$
$660$	1.66469	−	13.7100i	0.0647980	−	0.533659i
$661$	3.13372	−	2.77624i	0.121888	−	0.107983i	−0.599977	−	0.800017i	$-0.704824\pi$
$661$	3.13372	−	2.77624i	0.121888	−	0.107983i	0.721865	+	0.692034i	$0.243285\pi$
$662$	25.1055	+	22.2416i	0.975754	+	0.864443i
$663$	−2.96641	−	24.4306i	−0.115206	−	0.948806i
$664$	−7.74132	−	11.2152i	−0.300421	−	0.435236i
$665$	4.98355	+	41.0432i	0.193254	+	1.59159i
$666$	−0.217656	−	0.573912i	−0.00843400	−	0.0222386i
$667$	35.5187	−	31.4668i	1.37529	−	1.21840i
$668$	5.65724	+	2.96915i	0.218885	+	0.114880i
$669$	−6.90343	+	10.0013i	−0.266902	+	0.386674i
$670$	7.49605	+	3.93423i	0.289598	+	0.151993i
$671$	−5.51576	+	45.4263i	−0.212933	+	1.75366i
$672$	0.660752	−	5.44178i	0.0254891	−	0.209921i
$673$	−7.07673	−	3.71416i	−0.272788	−	0.143170i	0.322783	−	0.946473i	$-0.395382\pi$
$673$	−7.07673	−	3.71416i	−0.272788	−	0.143170i	−0.595571	+	0.803303i	$0.703074\pi$
$674$	−5.75997	+	8.34476i	−0.221866	+	0.321428i
$675$	−11.2155	−	5.88635i	−0.431685	−	0.226566i
$676$	−10.1475	+	8.98992i	−0.390289	+	0.345766i
$677$	−2.47795	−	6.53383i	−0.0952355	−	0.251115i	0.878930	−	0.476951i	$-0.158258\pi$
$677$	−2.47795	−	6.53383i	−0.0952355	−	0.251115i	−0.974165	+	0.225836i	$0.927489\pi$
$678$	−2.29901	−	18.9340i	−0.0882928	−	0.727157i
$679$	5.81328	+	8.42199i	0.223093	+	0.323206i
$680$	−0.559921	−	4.61136i	−0.0214720	−	0.176838i
$681$	4.64493	+	4.11505i	0.177994	+	0.157689i
$682$	−7.82511	+	6.93245i	−0.299639	+	0.265457i
$683$	3.37768	−	27.8177i	0.129243	−	1.06442i	−0.773367	−	0.633958i	$-0.781429\pi$
$683$	3.37768	−	27.8177i	0.129243	−	1.06442i	0.902611	−	0.430458i	$-0.141648\pi$
$684$	1.45360	−	0.762910i	0.0555799	−	0.0291706i
$685$	−10.4225	−	27.4818i	−0.398222	−	1.05003i
$686$	6.01028	+	8.70739i	0.229473	+	0.332450i
$687$	22.8077			0.870166
$688$	−4.56027			−0.173859
$689$	12.1868	+	17.6556i	0.464279	+	0.672624i
$690$	−15.1960	−	13.4624i	−0.578500	−	0.512507i
$691$	46.8358	+	11.5440i	1.78172	+	0.439154i	0.986032	−	0.166557i	$-0.0532650\pi$
$691$	46.8358	+	11.5440i	1.78172	+	0.439154i	0.795685	+	0.605711i	$0.207111\pi$
$692$	−6.49080	+	9.40355i	−0.246743	+	0.357469i
$693$	−2.01051	+	2.91272i	−0.0763729	+	0.110645i
$694$	−12.1483	+	2.99430i	−0.461145	+	0.113662i
$695$	23.5309	−	12.3500i	0.892577	−	0.468460i
$696$	7.92347	−	7.01958i	0.300338	−	0.266077i
$697$	−15.8189	−	3.89902i	−0.599185	−	0.147686i
$698$	−19.6497	+	4.84322i	−0.743753	+	0.183319i
$699$	2.37276	−	19.5415i	0.0897461	−	0.739126i
$700$	6.86537	−	3.60323i	0.259487	−	0.136189i
$701$	2.77767	−	7.32412i	0.104911	−	0.276628i	−0.872274	−	0.489018i	$-0.837355\pi$
$701$	2.77767	−	7.32412i	0.104911	−	0.276628i	0.977185	+	0.212390i	$0.0681246\pi$
$702$	20.6868	+	18.3269i	0.780772	+	0.691704i
$703$	−7.97119	−	21.0183i	−0.300639	−	0.792720i
$704$	1.80567	−	4.76116i	0.0680537	−	0.179443i
$705$	10.5108	+	2.59068i	0.395860	+	0.0975708i
$706$	11.3014	+	5.93145i	0.425335	+	0.223233i
$707$	25.3636	−	6.25156i	0.953895	−	0.235114i
$708$	−4.42959	+	11.6799i	−0.166474	+	0.438956i
$709$	5.70645	+	46.9968i	0.214310	+	1.76500i	0.561756	+	0.827303i	$0.310126\pi$
$709$	5.70645	+	46.9968i	0.214310	+	1.76500i	−0.347446	+	0.937700i	$0.612951\pi$
$710$	−17.4161			−0.653614
$711$	0.304230	+	1.85706i	0.0114095	+	0.0696452i
$712$	1.58181			0.0592808
$713$	1.85237	+	15.2556i	0.0693718	+	0.571328i
$714$	5.55929	−	14.6586i	0.208051	−	0.548585i
$715$	−41.3836	+	10.2001i	−1.54766	+	0.381464i
$716$	−4.44690	−	2.33391i	−0.166189	−	0.0872225i
$717$	27.7956	+	6.85101i	1.03805	+	0.255856i
$718$	−3.62441	+	9.55679i	−0.135262	+	0.356656i
$719$	1.37743	+	3.63199i	0.0513696	+	0.135450i	0.958245	−	0.285948i	$-0.0923086\pi$
$719$	1.37743	+	3.63199i	0.0513696	+	0.135450i	−0.906876	+	0.421399i	$0.861539\pi$
$720$	0.257403	+	0.228039i	0.00959285	+	0.00849853i
$721$	−10.2030	+	26.9031i	−0.379980	+	1.00193i
$722$	36.4115	−	19.1102i	1.35510	−	0.711209i
$723$	−2.59925	+	21.4068i	−0.0966672	+	0.796126i
$724$	24.1302	−	5.94755i	0.896790	−	0.221039i
$725$	14.5375	+	3.58316i	0.539908	+	0.133075i
$726$	18.6595	−	16.5308i	0.692518	−	0.613517i
$727$	−16.0231	+	8.40958i	−0.594265	+	0.311894i	−0.734909	−	0.678166i	$-0.762775\pi$
$727$	−16.0231	+	8.40958i	−0.594265	+	0.311894i	0.140644	+	0.990060i	$0.455083\pi$
$728$	−16.4261	+	4.04866i	−0.608790	+	0.150053i
$729$	16.2620	−	23.5596i	0.602297	−	0.872578i
$730$	6.54796	−	9.48636i	0.242351	−	0.351106i
$731$	−12.6631	−	3.12116i	−0.468360	−	0.115440i
$732$	11.2320	+	9.95072i	0.415148	+	0.367789i
$733$	27.1898	+	39.3912i	1.00428	+	1.45495i	0.886956	+	0.461854i	$0.152815\pi$
$733$	27.1898	+	39.3912i	1.00428	+	1.45495i	0.117322	+	0.993094i	$0.462569\pi$
$734$	5.31947			0.196345
$735$	−10.2443			−0.377865
$736$	−4.25214	−	6.16028i	−0.156736	−	0.227071i
$737$	9.41133	+	24.8156i	0.346671	+	0.914096i
$738$	1.06797	−	0.560514i	0.0393126	−	0.0206328i
$739$	−5.51288	+	45.4027i	−0.202795	+	1.67017i	0.435360	+	0.900257i	$0.356621\pi$
$739$	−5.51288	+	45.4027i	−0.202795	+	1.67017i	−0.638154	+	0.769908i	$0.720302\pi$
$740$	3.52463	−	3.12255i	0.129568	−	0.114787i
$741$	49.9426	+	44.2453i	1.83469	+	1.62539i
$742$	1.64730	+	13.5667i	0.0604742	+	0.498050i
$743$	−18.3240	−	26.5469i	−0.672242	−	0.973910i	−0.999579	−	0.0290026i	$-0.990767\pi$
$743$	−18.3240	−	26.5469i	−0.672242	−	0.973910i	0.327338	−	0.944907i	$-0.393848\pi$
$744$	0.413225	+	3.40321i	0.0151496	+	0.124768i
$745$	−1.40057	−	3.69299i	−0.0513128	−	0.135301i
$746$	−11.2543	+	9.97041i	−0.412048	+	0.365043i
$747$	2.55475	+	1.34083i	0.0934732	+	0.0490585i
$748$	8.27268	−	11.9850i	0.302479	−	0.438217i
$749$	−20.8226	−	10.9286i	−0.760842	−	0.399321i
$750$	2.40672	−	19.8211i	0.0878808	−	0.723764i
$751$	0.0664021	−	0.546871i	0.00242305	−	0.0199556i	−0.991447	−	0.130508i	$-0.958339\pi$
$751$	0.0664021	−	0.546871i	0.00242305	−	0.0199556i	0.993870	+	0.110553i	$0.0352621\pi$
$752$	3.53419	+	1.85488i	0.128879	+	0.0676407i
$753$	−24.4390	+	35.4059i	−0.890605	+	1.29026i
$754$	−28.9271	−	15.1821i	−1.05346	−	0.552901i
$755$	21.4218	−	18.9781i	0.779620	−	0.690683i
$756$	6.24312	+	16.4618i	0.227060	+	0.598708i
$757$	5.56895	+	45.8644i	0.202407	+	1.66697i	0.640438	+	0.768010i	$0.278753\pi$
$757$	5.56895	+	45.8644i	0.202407	+	1.66697i	−0.438031	+	0.898960i	$0.644324\pi$
$758$	−9.98722	−	14.4690i	−0.362752	−	0.525537i
$759$	−7.67168	−	63.1819i	−0.278464	−	2.29336i
$760$	9.42685	+	8.35146i	0.341948	+	0.302939i
$761$	−26.4552	+	23.4373i	−0.959002	+	0.849601i	−0.988692	−	0.149958i	$-0.952086\pi$
$761$	−26.4552	+	23.4373i	−0.959002	+	0.849601i	0.0296906	+	0.999559i	$0.490548\pi$
$762$	0.439702	−	3.62127i	0.0159287	−	0.131185i
$763$	5.77930	−	3.03321i	0.209225	−	0.109810i
$764$	6.81308	+	17.9646i	0.246489	+	0.649937i
$765$	0.558687	+	0.809398i	0.0201994	+	0.0292639i
$766$	−8.81762			−0.318593
$767$	38.5513			1.39201
$768$	−0.948563	−	1.37423i	−0.0342283	−	0.0495883i
$769$	−0.987370	−	0.874733i	−0.0356055	−	0.0315437i	0.645132	−	0.764071i	$-0.276802\pi$
$769$	−0.987370	−	0.874733i	−0.0356055	−	0.0315437i	−0.680738	+	0.732527i	$0.738341\pi$
$770$	−26.3627	−	6.49783i	−0.950047	−	0.234166i
$771$	17.2424	−	24.9800i	0.620970	−	0.899631i
$772$	1.48468	−	2.15093i	0.0534348	−	0.0774137i
$773$	53.3188	−	13.1419i	1.91774	−	0.472681i	0.921254	−	0.388961i	$-0.127166\pi$
$773$	53.3188	−	13.1419i	1.91774	−	0.472681i	0.996489	−	0.0837206i	$-0.0266803\pi$
$774$	0.854911	−	0.448692i	0.0307291	−	0.0161279i
$775$	−3.62947	+	3.21543i	−0.130374	+	0.115502i
$776$	3.02667	+	0.746008i	0.108651	+	0.0267801i
$777$	15.4303	−	3.80323i	0.553560	−	0.136440i
$778$	−0.920922	+	7.58448i	−0.0330167	+	0.271917i
$779$	39.1122	−	20.5276i	1.40134	−	0.735479i
$780$	−4.95626	+	13.0686i	−0.177463	+	0.467931i
$781$	−40.8686	−	36.2064i	−1.46239	−	1.29557i
$782$	−7.59118	−	20.0163i	−0.271460	−	0.715781i
$783$	−12.0559	+	31.7888i	−0.430843	+	1.13604i
$784$	−3.66735	−	0.903922i	−0.130977	−	0.0322829i
$785$	−2.49686	−	1.31046i	−0.0891169	−	0.0467722i
$786$	−1.47532	+	0.363635i	−0.0526231	+	0.0129704i
$787$	5.86697	−	15.4699i	0.209135	−	0.551444i	−0.788871	−	0.614558i	$-0.789334\pi$
$787$	5.86697	−	15.4699i	0.209135	−	0.551444i	0.998006	+	0.0631148i	$0.0201034\pi$
$788$	−1.48310	−	12.2145i	−0.0528334	−	0.435122i
$789$	17.1482			0.610491
$790$	−12.4933	+	7.23424i	−0.444491	+	0.257383i
$791$	−37.4977			−1.33326
$792$	0.129950	+	1.07023i	0.00461757	+	0.0380291i
$793$	16.4220	−	43.3013i	0.583162	−	1.53767i
$794$	−34.9637	+	8.61778i	−1.24082	+	0.305834i
$795$	9.99746	+	5.24707i	0.354573	+	0.186094i
$796$	−14.9068	−	3.67419i	−0.528357	−	0.130228i
$797$	−0.307426	+	0.810616i	−0.0108896	+	0.0287135i	−0.940351	−	0.340206i	$-0.889503\pi$
$797$	−0.307426	+	0.810616i	−0.0108896	+	0.0287135i	0.929461	+	0.368920i	$0.120272\pi$
$798$	15.0723	+	39.7424i	0.533554	+	1.40687i
$799$	8.54428	+	7.56957i	0.302275	+	0.267792i
$800$	0.837511	−	2.20834i	0.0296105	−	0.0780765i
$801$	−0.296541	+	0.155637i	−0.0104778	+	0.00549915i
$802$	2.79568	−	23.0245i	0.0987190	−	0.813024i
$803$	35.0867	−	8.64810i	1.23818	−	0.305185i
$804$	8.45034	+	2.08282i	0.298020	+	0.0734554i
$805$	−29.8752	+	26.4671i	−1.05296	+	0.932844i
$806$	9.36818	−	4.91680i	0.329980	−	0.173187i
$807$	−16.1803	+	3.98808i	−0.569573	+	0.140387i
$808$	4.52026	−	6.54873i	0.159022	−	0.230384i
$809$	12.6992	−	18.3979i	0.446479	−	0.646836i	−0.533532	−	0.845780i	$-0.679136\pi$
$809$	12.6992	−	18.3979i	0.446479	−	0.646836i	0.980011	+	0.198944i	$0.0637511\pi$
$810$	13.1211	+	3.23406i	0.461028	+	0.113633i
$811$	9.98317	+	8.84431i	0.350556	+	0.310566i	0.819963	−	0.572416i	$-0.193994\pi$
$811$	9.98317	+	8.84431i	0.350556	+	0.310566i	−0.469407	+	0.882982i	$0.655532\pi$
$812$	−11.8222	−	17.1274i	−0.414878	−	0.601054i
$813$	14.2668			0.500358
$814$	14.7624			0.517421
$815$	13.6998	+	19.8477i	0.479885	+	0.695233i
$816$	−1.69343	−	4.46521i	−0.0592820	−	0.156314i
$817$	31.3093	−	16.4324i	1.09537	−	0.574896i
$818$	−2.78629	+	22.9471i	−0.0974202	+	0.802328i
$819$	2.68103	−	2.37519i	0.0936828	−	0.0829957i
$820$	6.92596	+	6.13586i	0.241865	+	0.214274i
$821$	−3.40579	−	28.0492i	−0.118863	−	0.978924i	−0.923085	−	0.384596i	$-0.874341\pi$
$821$	−3.40579	−	28.0492i	−0.118863	−	0.978924i	0.804222	−	0.594329i	$-0.202582\pi$
$822$	−17.1648	−	24.8676i	−0.598692	−	0.867356i
$823$	−1.54265	−	12.7049i	−0.0537734	−	0.442864i	−0.994584	−	0.103932i	$-0.966858\pi$
$823$	−1.54265	−	12.7049i	−0.0537734	−	0.442864i	0.940811	−	0.338932i	$-0.110066\pi$
$824$	3.10797	+	8.19505i	0.108271	+	0.285488i
$825$	15.0316	−	13.3168i	0.523334	−	0.463633i
$826$	21.7455	+	11.4129i	0.756621	+	0.397105i
$827$	4.47838	−	6.48805i	0.155728	−	0.225611i	−0.737352	−	0.675509i	$-0.763924\pi$
$827$	4.47838	−	6.48805i	0.155728	−	0.225611i	0.893080	+	0.449897i	$0.148539\pi$
$828$	1.40327	+	0.736490i	0.0487668	+	0.0255948i
$829$	5.66122	−	46.6244i	0.196622	−	1.61933i	−0.476069	−	0.879408i	$-0.657939\pi$
$829$	5.66122	−	46.6244i	0.196622	−	1.61933i	0.672691	−	0.739923i	$-0.265138\pi$
$830$	−2.66802	+	21.9731i	−0.0926083	+	0.762698i
$831$	21.3543	+	11.2076i	0.740771	+	0.388787i
$832$	−2.92743	+	4.24112i	−0.101490	+	0.147034i
$833$	−9.56493	−	5.02006i	−0.331405	−	0.173935i
$834$	20.4496	−	18.1168i	0.708111	−	0.627332i
$835$	−3.67989	−	9.70307i	−0.127348	−	0.335789i
$836$	4.75914	+	39.1950i	0.164598	+	1.35559i
$837$	−6.25465	−	9.06142i	−0.216192	−	0.313208i
$838$	−1.97285	−	16.2479i	−0.0681511	−	0.561275i
$839$	−17.0062	−	15.0662i	−0.587118	−	0.520141i	0.316437	−	0.948614i	$-0.397514\pi$
$839$	−17.0062	−	15.0662i	−0.587118	−	0.520141i	−0.903555	+	0.428472i	$0.859052\pi$
$840$	−6.66454	+	5.90426i	−0.229948	+	0.203716i
$841$	1.34859	−	11.1066i	0.0465031	−	0.382988i
$842$	−6.25250	+	3.28157i	−0.215475	+	0.113090i
$843$	−0.0693956	−	0.182981i	−0.00239011	−	0.00630220i
$844$	−14.1208	−	20.4576i	−0.486059	−	0.704178i
$845$	22.0199			0.757506
$846$	−0.845057			−0.0290537
$847$	−27.8408	−	40.3344i	−0.956622	−	1.38591i
$848$	3.11602	+	2.76055i	0.107004	+	0.0947977i
$849$	−37.9814	−	9.36158i	−1.30352	−	0.321289i
$850$	3.83706	−	5.55894i	0.131610	−	0.190670i
$851$	12.3274	−	17.8593i	0.422576	−	0.612207i
$852$	−17.3844	+	4.28486i	−0.595579	+	0.146797i
$853$	1.88014	−	0.986774i	0.0643748	−	0.0337865i	−0.432229	−	0.901764i	$-0.642273\pi$
$853$	1.88014	−	0.986774i	0.0643748	−	0.0337865i	0.496603	+	0.867978i	$0.334580\pi$
$854$	22.0822	−	19.5631i	0.755636	−	0.669435i
$855$	−2.58896	−	0.638121i	−0.0885405	−	0.0218233i
$856$	−6.95522	+	1.71431i	−0.237724	+	0.0585938i
$857$	2.50630	−	20.6412i	0.0856135	−	0.705090i	−0.885193	−	0.465225i	$-0.845974\pi$
$857$	2.50630	−	20.6412i	0.0856135	−	0.705090i	0.970806	−	0.239866i	$-0.0771034\pi$
$858$	−38.7987	+	20.3632i	−1.32457	+	0.695187i
$859$	−19.7124	+	51.9772i	−0.672577	+	1.77344i	−0.0396677	+	0.999213i	$0.512630\pi$
$859$	−19.7124	+	51.9772i	−0.672577	+	1.77344i	−0.632909	+	0.774226i	$0.718139\pi$
$860$	5.54423	+	4.91176i	0.189057	+	0.167489i
$861$	11.0737	+	29.1990i	0.377391	+	0.995098i
$862$	1.15339	−	3.04125i	0.0392847	−	0.103585i
$863$	53.2204	+	13.1177i	1.81164	+	0.446530i	0.991989	−	0.126326i	$-0.0403186\pi$
$863$	53.2204	+	13.1177i	1.81164	+	0.446530i	0.819656	+	0.572857i	$0.194165\pi$
$864$	4.74868	+	2.49230i	0.161553	+	0.0847898i
$865$	18.0197	−	4.44145i	0.612687	−	0.151014i
$866$	3.24288	−	8.55078i	0.110198	−	0.290567i
$867$	1.77540	+	14.6217i	0.0602957	+	0.496580i
$868$	6.73985			0.228765
$869$	−44.3561	−	8.99651i	−1.50468	−	0.305186i
$870$	−17.1937			−0.582922
$871$	−3.23758	−	26.6639i	−0.109701	−	0.903472i
$872$	0.705020	−	1.85899i	0.0238750	−	0.0629532i
$873$	−0.640809	+	0.157945i	−0.0216881	+	0.00534564i
$874$	51.3916	+	26.9724i	1.73835	+	0.912355i
$875$	−38.1138	−	9.39420i	−1.28848	−	0.317582i
$876$	4.20212	−	11.0801i	0.141977	−	0.374361i
$877$	−11.5691	−	30.5053i	−0.390662	−	1.03009i	−0.975705	−	0.219088i	$-0.929692\pi$
$877$	−11.5691	−	30.5053i	−0.390662	−	1.03009i	0.585044	−	0.811002i	$-0.301077\pi$
$878$	17.4275	+	15.4394i	0.588150	+	0.521055i
$879$	3.08557	−	8.13599i	0.104074	−	0.274420i
$880$	−7.32341	+	3.84362i	−0.246872	+	0.129568i
$881$	−0.727338	+	5.99017i	−0.0245047	+	0.201814i	−0.999819	−	0.0190054i	$-0.993950\pi$
$881$	−0.727338	+	5.99017i	−0.0245047	+	0.201814i	0.975315	+	0.220819i	$0.0708731\pi$
$882$	0.776455	−	0.191379i	0.0261446	−	0.00644407i
$883$	−42.7264	−	10.5311i	−1.43786	−	0.354400i	−0.558080	−	0.829787i	$-0.688462\pi$
$883$	−42.7264	−	10.5311i	−1.43786	−	0.354400i	−0.879777	+	0.475387i	$0.842308\pi$
$884$	−11.0317	+	9.77322i	−0.371036	+	0.328709i
$885$	17.9654	−	9.42899i	0.603902	−	0.316952i
$886$	3.69439	−	0.910586i	0.124115	−	0.0305917i
$887$	−6.33392	+	9.17626i	−0.212672	+	0.308109i	−0.914773	−	0.403969i	$-0.867630\pi$
$887$	−6.33392	+	9.17626i	−0.212672	+	0.308109i	0.702100	+	0.712078i	$0.252246\pi$
$888$	2.74997	−	3.98403i	0.0922831	−	0.133695i
$889$	−6.96330	−	1.71630i	−0.233542	−	0.0575628i
$890$	−1.92311	−	1.70373i	−0.0644629	−	0.0571091i
$891$	24.0666	+	34.8665i	0.806263	+	1.16807i
$892$	7.27778			0.243678
$893$	−30.9484			−1.03565
$894$	−2.30660	−	3.34169i	−0.0771443	−	0.111763i
$895$	2.89260	+	7.62715i	0.0966888	+	0.254947i
$896$	−2.90682	+	1.52562i	−0.0971100	+	0.0509673i
$897$	−7.76400	+	63.9423i	−0.259233	+	2.13497i
$898$	12.1873	−	10.7970i	0.406696	−	0.360301i
$899$	9.74196	+	8.63063i	0.324913	+	0.287847i
$900$	0.0602738	+	0.496399i	0.00200913	+	0.0165466i
$901$	6.76324	+	9.79824i	0.225316	+	0.326427i
$902$	3.49657	+	28.7968i	0.116423	+	0.958829i
$903$	8.86450	+	23.3738i	0.294992	+	0.777830i
$904$	−8.54970	+	7.57437i	−0.284359	+	0.251920i
$905$	−35.7426	−	18.7592i	−1.18813	−	0.623576i
$906$	16.7137	−	24.2139i	0.555274	−	0.804454i
$907$	−44.6417	−	23.4298i	−1.48230	−	0.777973i	−0.486874	−	0.873472i	$-0.661863\pi$
$907$	−44.6417	−	23.4298i	−1.48230	−	0.777973i	−0.995429	+	0.0954994i	$0.969555\pi$
$908$	0.447953	−	3.68922i	0.0148658	−	0.122431i
$909$	−0.203071	+	1.67244i	−0.00673545	+	0.0554714i
$910$	24.3310	+	12.7699i	0.806565	+	0.423318i
$911$	4.89135	−	7.08634i	0.162058	−	0.234781i	−0.733540	−	0.679646i	$-0.762133\pi$
$911$	4.89135	−	7.08634i	0.162058	−	0.234781i	0.895597	+	0.444866i	$0.146749\pi$
$912$	11.4644	+	6.01697i	0.379624	+	0.199242i
$913$	−51.9408	+	46.0155i	−1.71899	+	1.52289i
$914$	4.90159	+	12.9244i	0.162130	+	0.427502i
$915$	−2.93787	−	24.1955i	−0.0971229	−	0.799879i
$916$	−7.75908	−	11.2410i	−0.256367	−	0.371412i
$917$	0.360078	+	2.96551i	0.0118908	+	0.0979297i
$918$	11.4805	+	10.1708i	0.378911	+	0.335686i
$919$	14.9494	−	13.2440i	0.493135	−	0.436880i	−0.379544	−	0.925174i	$-0.623919\pi$
$919$	14.9494	−	13.2440i	0.493135	−	0.436880i	0.872679	+	0.488294i	$0.162381\pi$
$920$	−1.46548	+	12.0694i	−0.0483156	+	0.397915i
$921$	30.7923	−	16.1611i	1.01464	−	0.532525i
$922$	2.32455	+	6.12933i	0.0765549	+	0.201859i
$923$	31.3895	+	45.4756i	1.03320	+	1.49685i
$924$	−27.9134			−0.918284
$925$	6.84713			0.225132
$926$	−3.12317	−	4.52469i	−0.102634	−	0.148690i
$927$	−1.38897	−	1.23052i	−0.0456199	−	0.0404157i
$928$	−6.15521	−	1.51712i	−0.202055	−	0.0498020i
$929$	13.9659	−	20.2332i	0.458208	−	0.663829i	−0.523980	−	0.851731i	$-0.675553\pi$
$929$	13.9659	−	20.2332i	0.458208	−	0.663829i	0.982188	+	0.187902i	$0.0601687\pi$
$930$	3.16313	−	4.58259i	0.103723	−	0.150269i
$931$	28.4360	−	7.00885i	0.931953	−	0.229706i
$932$	−10.4384	+	5.47849i	−0.341921	+	0.179454i
$933$	−31.9048	+	28.2652i	−1.04452	+	0.925361i
$934$	−12.1771	−	3.00139i	−0.398447	−	0.0982084i
$935$	−22.9665	+	5.66073i	−0.751084	+	0.185126i
$936$	0.131514	−	1.08311i	0.00429867	−	0.0354027i
$937$	−8.84854	+	4.64407i	−0.289069	+	0.151715i	−0.603025	−	0.797722i	$-0.706038\pi$
$937$	−8.84854	+	4.64407i	−0.289069	+	0.151715i	0.313956	+	0.949438i	$0.398346\pi$
$938$	6.06748	−	15.9986i	0.198110	−	0.522374i
$939$	−41.5840	−	36.8402i	−1.35704	−	1.20223i
$940$	−2.29890	−	6.06170i	−0.0749818	−	0.197711i
$941$	−15.7916	+	41.6389i	−0.514790	+	1.35739i	0.385744	+	0.922606i	$0.373945\pi$
$941$	−15.7916	+	41.6389i	−0.514790	+	1.35739i	−0.900534	+	0.434785i	$0.856824\pi$
$942$	−2.81473	−	0.693769i	−0.0917089	−	0.0226042i
$943$	37.7577	+	19.8168i	1.22956	+	0.645323i
$944$	7.26346	−	1.79028i	0.236405	−	0.0582687i
$945$	10.1404	−	26.7380i	0.329867	−	0.869787i
$946$	2.79900	+	23.0518i	0.0910034	+	0.749480i
$947$	−29.6662			−0.964023			−0.482011	−	0.876165i	$-0.660094\pi$
$947$	−29.6662			−0.964023			−0.482011	+	0.876165i	$0.660094\pi$
$948$	−10.6907	+	10.2948i	−0.347218	+	0.334359i
$949$	−36.5717			−1.18717
$950$	2.20740	+	18.1796i	0.0716175	+	0.589823i
$951$	−15.2349	+	40.1711i	−0.494025	+	1.30264i
$952$	−9.11590	+	2.24687i	−0.295448	+	0.0728214i
$953$	−36.3005	−	19.0520i	−1.17589	−	0.617154i	−0.240456	−	0.970660i	$-0.577297\pi$
$953$	−36.3005	−	19.0520i	−1.17589	−	0.617154i	−0.935432	+	0.353506i	$0.884989\pi$
$954$	−0.855773	−	0.210929i	−0.0277067	−	0.00682908i
$955$	11.0661	−	29.1790i	0.358092	−	0.944211i
$956$	−6.07939	−	16.0300i	−0.196621	−	0.518448i
$957$	−40.3468	−	35.7441i	−1.30423	−	1.15544i
$958$	−2.70702	+	7.13783i	−0.0874599	+	0.230613i
$959$	−52.6007	+	27.6070i	−1.69857	+	0.891476i
$960$	−0.326919	+	2.69242i	−0.0105513	+	0.0868974i
$961$	26.0067	−	6.41007i	0.838925	−	0.206776i
$962$	−14.5059	−	3.57539i	−0.467689	−	0.115275i
$963$	1.13522	−	1.00571i	0.0365819	−	0.0324087i
$964$	11.4348	−	6.00143i	0.368289	−	0.193293i
$965$	−4.12174	+	1.01592i	−0.132684	+	0.0327036i
$966$	−23.3092	+	33.7691i	−0.749960	+	1.08650i
$967$	23.3769	−	33.8673i	0.751751	−	1.08910i	−0.241189	−	0.970478i	$-0.577537\pi$
$967$	23.3769	−	33.8673i	0.751751	−	1.08910i	0.992940	−	0.118621i	$-0.0378473\pi$
$968$	−14.4953	−	3.57276i	−0.465896	−	0.114833i
$969$	27.7164	+	24.5546i	0.890379	+	0.788807i
$970$	−2.87622	−	4.16693i	−0.0923499	−	0.133792i
$971$	−10.2051			−0.327498			−0.163749	−	0.986502i	$-0.552359\pi$
$971$	−10.2051			−0.327498			−0.163749	+	0.986502i	$0.552359\pi$
$972$	−2.19606			−0.0704385
$973$	−30.5118	−	44.2039i	−0.978163	−	1.41711i
$974$	1.06807	+	2.81627i	0.0342232	+	0.0902390i
$975$	−17.9958	+	9.44490i	−0.576325	+	0.302479i
$976$	1.08321	−	8.92102i	0.0346726	−	0.285555i
$977$	36.6143	−	32.4374i	1.17139	−	1.03776i	0.172789	−	0.984959i	$-0.444722\pi$
$977$	36.6143	−	32.4374i	1.17139	−	1.03776i	0.998605	−	0.0528059i	$-0.0168165\pi$
$978$	18.5580	+	16.4410i	0.593420	+	0.525724i
$979$	−0.970883	−	7.99594i	−0.0310296	−	0.255551i
$980$	3.48506	+	5.04898i	0.111326	+	0.161284i
$981$	0.0507387	+	0.417871i	0.00161996	+	0.0133416i
$982$	4.45785	+	11.7544i	0.142256	+	0.375098i
$983$	−8.29642	+	7.34999i	−0.264615	+	0.234428i	−0.784988	−	0.619510i	$-0.787331\pi$
$983$	−8.29642	+	7.34999i	−0.264615	+	0.234428i	0.520374	+	0.853939i	$0.325793\pi$
$984$	8.42295	+	4.42070i	0.268514	+	0.140927i
$985$	−11.3528	+	16.4474i	−0.361730	+	0.524057i
$986$	−16.0536	−	8.42556i	−0.511249	−	0.268324i
$987$	2.63731	−	21.7202i	0.0839465	−	0.691361i
$988$	4.81642	−	39.6668i	0.153231	−	1.26197i
$989$	30.2250	+	15.8633i	0.961100	+	0.504424i
$990$	0.994735	−	1.44112i	0.0316148	−	0.0458019i
$991$	15.8549	+	8.32128i	0.503647	+	0.264334i	0.697356	−	0.716725i	$-0.254360\pi$
$991$	15.8549	+	8.32128i	0.503647	+	0.264334i	−0.193709	+	0.981059i	$0.562052\pi$
$992$	1.53673	−	1.36142i	0.0487912	−	0.0432252i
$993$	−19.8602	−	52.3671i	−0.630245	−	1.66182i
$994$	4.24295	+	34.9439i	0.134578	+	1.10835i
$995$	14.1658	+	20.5227i	0.449086	+	0.650614i
$996$	2.74287	+	22.5895i	0.0869110	+	0.715777i
$997$	15.3367	+	13.5872i	0.485719	+	0.430309i	0.870108	−	0.492862i	$-0.164049\pi$
$997$	15.3367	+	13.5872i	0.485719	+	0.430309i	−0.384389	+	0.923171i	$0.625588\pi$
$998$	23.6223	−	20.9275i	0.747749	−	0.662448i
$999$	−1.87408	+	15.4344i	−0.0592932	+	0.488324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	158.2.e.a.67.4	✓	48
79.46	even	13	inner	158.2.e.a.125.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
158.2.e.a.67.4	✓	48	1.1	even	1	trivial
158.2.e.a.125.4	yes	48	79.46	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	158.e (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.120537 + 0.992709i) q^{2} +(0.592124 - 1.56130i) q^{3} +(-0.970942 + 0.239316i) q^{4} +(1.43820 + 0.754826i) q^{5} +(1.62129 + 0.399613i) q^{6} +(1.16412 - 3.06952i) q^{7} +(-0.354605 - 0.935016i) q^{8} +(0.158475 + 0.140397i) q^{9} +(-0.575967 + 1.51870i) q^{10} +(-4.50880 + 2.36640i) q^{11} +(-0.201274 + 1.65764i) q^{12} +(5.00360 - 1.23328i) q^{13} +(3.18746 + 0.785638i) q^{14} +(2.03011 - 1.79852i) q^{15} +(0.885456 - 0.464723i) q^{16} +(2.77682 - 0.684425i) q^{17} +(-0.120271 + 0.174243i) q^{18} +(-4.40467 + 6.38127i) q^{19} +(-1.57705 - 0.388708i) q^{20} +(-4.10315 - 3.63507i) q^{21} +(-2.89262 - 4.19068i) q^{22} -7.48530 q^{23} -1.66981 q^{24} +(-1.34166 - 1.94374i) q^{25} +(1.82740 + 4.81846i) q^{26} +(4.74868 - 2.49230i) q^{27} +(-0.395704 + 3.25892i) q^{28} +(-4.74512 + 4.20381i) q^{29} +(2.03011 + 1.79852i) q^{30} +(-0.247468 - 2.03808i) q^{31} +(0.568065 + 0.822984i) q^{32} +(1.02490 + 8.44080i) q^{33} +(1.01414 + 2.67408i) q^{34} +(3.99118 - 3.53588i) q^{35} +(-0.187469 - 0.0983915i) q^{36} +(-1.64687 + 2.38591i) q^{37} +(-6.86567 - 3.60338i) q^{38} +(1.03723 - 8.54238i) q^{39} +(0.195782 - 1.61241i) q^{40} +(-5.04424 - 2.64742i) q^{41} +(3.11399 - 4.51139i) q^{42} +(-4.03792 - 2.11926i) q^{43} +(3.81146 - 3.37666i) q^{44} +(0.121944 + 0.321540i) q^{45} +(-0.902254 - 7.43073i) q^{46} +(2.26736 + 3.28484i) q^{47} +(-0.201274 - 1.65764i) q^{48} +(-2.82721 - 2.50469i) q^{49} +(1.76784 - 1.56617i) q^{50} +(0.575629 - 4.74073i) q^{51} +(-4.56306 + 2.39488i) q^{52} +(1.47620 + 3.89243i) q^{53} +(3.04652 + 4.41364i) q^{54} -8.27077 q^{55} -3.28285 q^{56} +(7.35498 + 10.6555i) q^{57} +(-4.74512 - 4.20381i) q^{58} +(7.26346 + 1.79028i) q^{59} +(-1.54070 + 2.23209i) q^{60} +(5.10493 - 7.39577i) q^{61} +(1.99339 - 0.491326i) q^{62} +(0.615434 - 0.323005i) q^{63} +(-0.748511 + 0.663123i) q^{64} +(8.12709 + 2.00315i) q^{65} +(-8.25572 + 2.03485i) q^{66} +(0.628249 - 5.17410i) q^{67} +(-2.53234 + 1.32907i) q^{68} +(-4.43223 + 11.6868i) q^{69} +(3.99118 + 3.53588i) q^{70} +(3.80227 + 10.0257i) q^{71} +(0.0750772 - 0.197962i) q^{72} +(-6.89047 - 1.69835i) q^{73} +(-2.56702 - 1.34728i) q^{74} +(-3.82919 + 0.943811i) q^{75} +(2.74954 - 7.24995i) q^{76} +(2.01495 + 16.5946i) q^{77} +8.60512 q^{78} +(6.89199 + 5.61252i) q^{79} +1.62425 q^{80} +(-1.00287 - 8.25935i) q^{81} +(2.02010 - 5.32658i) q^{82} +(13.2315 - 3.26128i) q^{83} +(4.85385 + 2.54750i) q^{84} +(4.51025 + 1.11168i) q^{85} +(1.61709 - 4.26392i) q^{86} +(3.75372 + 9.89775i) q^{87} +(3.81146 + 3.37666i) q^{88} +(-0.560917 + 1.47902i) q^{89} +(-0.304497 + 0.159812i) q^{90} +(2.03920 - 16.7943i) q^{91} +(7.26779 - 1.79135i) q^{92} +(-3.32859 - 0.820424i) q^{93} +(-2.98759 + 2.64677i) q^{94} +(-11.1516 + 5.85279i) q^{95} +(1.62129 - 0.399613i) q^{96} +(-1.77080 + 2.56545i) q^{97} +(2.14564 - 3.10850i) q^{98} +(-1.04677 - 0.258005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 8 q^{7} - 4 q^{8} - 18 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{12} + 16 q^{13} + 5 q^{14} - 2 q^{15} - 4 q^{16} + 6 q^{17} - 18 q^{18} + 6 q^{19} - 2 q^{20}+ \cdots - 58 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 8 * q^7 - 4 * q^8 - 18 * q^9 - 2 * q^10 - 8 * q^11 - 2 * q^12 + 16 * q^13 + 5 * q^14 - 2 * q^15 - 4 * q^16 + 6 * q^17 - 18 * q^18 + 6 * q^19 - 2 * q^20 - 12 * q^21 + 5 * q^22 - 16 * q^23 + 24 * q^24 - 17 * q^25 + 3 * q^26 + 7 * q^27 - 8 * q^28 - 34 * q^29 - 2 * q^30 - 19 * q^31 - 4 * q^32 + 8 * q^33 - 20 * q^34 + 122 * q^35 - 18 * q^36 - 4 * q^37 - 20 * q^38 - 50 * q^39 - 2 * q^40 - 36 * q^41 + 14 * q^42 - 24 * q^43 + 18 * q^44 - 4 * q^45 + 10 * q^46 - 22 * q^47 - 2 * q^48 - 28 * q^49 - 4 * q^50 + 78 * q^51 - 10 * q^52 - 12 * q^53 + 7 * q^54 - 88 * q^55 + 18 * q^56 - 28 * q^57 - 34 * q^58 - 52 * q^59 + 11 * q^60 - 47 * q^61 + 20 * q^62 + 11 * q^63 - 4 * q^64 - 16 * q^65 + 8 * q^66 + 67 * q^67 - 7 * q^68 - 4 * q^69 + 122 * q^70 - 12 * q^71 - 18 * q^72 + 101 * q^73 - 4 * q^74 - 62 * q^75 + 32 * q^76 + 113 * q^77 - 50 * q^78 - 2 * q^80 + 36 * q^81 + 29 * q^82 + 91 * q^83 + 53 * q^84 - q^85 - 24 * q^86 + 210 * q^87 + 18 * q^88 + 4 * q^89 + 126 * q^90 - 33 * q^91 - 3 * q^92 - 3 * q^93 + 17 * q^94 - 42 * q^95 - 2 * q^96 - 32 * q^97 + 24 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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